As far as I know, there isn't one, single, stance on Amida Buddha and which "kaya" or body he is identified with.
All Buddhas possess all the same wisdom, powers, and marks according to the sutras.
While the names bodies are rarely even mentioned altogether in sutras, it's generally recognized that all Buddhas manifest all three.
In fact, some say that the Trikaya doctrine wasn't explicitly spelled out until the Yogacarans did it in the 3rd century CE.
So finding explicit sutra references in regards to this question can be a little tricky and must rely on interpretation.
The Nirmanakaya is the transformation or manifestation body, the physical body that all beings can see.
Example: Aside from perhaps the Lotus Sutra, Shakyamuni is generally considered a supreme Nirmanakaya.
The Sambhogakaya is also called the reward body or the bliss body and can only be known by those with the right karmic conditions.
Buddhas associated with Pure Lands and fulfilling vows, such as Medicine Buddha are commonly typed as Sambhogakaya Buddhas.
The Dharmakaya is "the body of reality itself, without specific, delimited form, wherein the Buddha is identified with the spiritually charged nature of everything that is." (Reginald Ray "Secret of the Vajra World" p 13) The Dharmakaya can really only be known by Buddhas, the other 2 bodies are "simply ways in which the Dharmakaya appears to people." (Harvey, "An Introduction to Buddhism" p 169).
Vairocana is described in the Brahma Net sutra as the original body (Dharma kaya) of Shakyamuni.
The Avatamsaka (ch 3) also describes Vairocana as the samadhi that is the seed body common to all Buddhas.
When it comes to Amida, different masters held different views as to which "Buddha body" that followers should identify with Amida.
Amida as Nirmanakaya
Member Sinweiy offered this insight, which I think is common in Chinese Buddhism.
He goes on to explain this a little more:Sinweiy wrote:Amitabha is an Emanation body; the corresponding Enjoyment body is Amitayus, "infinite life"-propitiated for longevity; the Dharma body is known as Ananta-prabha, "boundless illumination."
Sinweiy wrote:Moreover, Shariputra, the lifespan of that Buddha and that of his people extends for measureless, limitless asamkhyeyas of kalpas. For this reason he is called Amitayus. And, Shariputra, since Amitabha became a Buddha, ten kalpas have passed. --Amitabha Sutra
here, two different names are use. Amitayus and Amitabha. Amitayus is without end, but a start, hence a Sambogakaya. Amitabha became Buddha ten kalpas ago and will have a "lifespan" of measureless, limitless asamkhyeyas of kalpas, hence an Nirmanakaya. Nirmanakaya has a start and an end to it.
all Buddhas have the three kayas. just different in naming. if one see it as Dharmakaya, then Amitabha is Anantaprabha. Amitabha is Dharmakaya. Dharmakaya is without start nor an end to it.
Amida as SambhogakayaSinweiy wrote:In the Mahayana Uttara Tantra Shastra (translated as 'The Changeless Nature'), it is explained that even though there is only one moon in the sky, it is reflected many times in pools and oceans, in clear or dirty water. Just like that example, Amitabha's activity permeates everywhere. The dharmakaya appears everywhere, dependent on the clarity of one's mind. If the water is agitated, the moon will still reflect in it, but unclearly. It is the same with one's mind: if the mind is agitated, the dharmakaya is not clearly revealed. That concludes the praise and homage to the dharmakaya.
Amitabha's speech is called Vajra Speech as it is unceasing. In terms of the quality of his speech, it is unequalled even by the sound of thunder, and also it is very beautiful, like melodious song or music. When the Buddha teaches, to those nearby his speech does not sound loud, but pleasant and clear, yet those listening far away can also hear it clearly. If one is listening to Amitabha's speech, it never sounds unpleasant, and it possesses 60 special qualities unmatched by melodious song. Rinpoché thinks that this is why the 2 examples, of his voice being unmatched by thunder and melodious song, are given in the sadhana. Out of compassion for all beings, Amitabha continually gives Dharma teachings. That is the praise and homage to the sambhogakaya.
There follows a praise to Amitabha's Vajra Mind, which is endowed with the 2 qualities of knowing the nature of things just as they are, and the many things that are to be known. It is a mind that cares for the welfare of all beings continually with great compassion and impartiality. Even though Brahma is a lord of a thousand million worlds, and Indra is powerful and has great merit, their minds cannot equal the mind of a buddha. One pays homage to Amitabha's mind, residing in a nirmanakaya form. In the text, it describes Amitabha as nirmanakaya, sambhogakaya or dharmakaya. These 3 are simply different aspects of forms. Each kaya has 3 different facets. For example, the dharmakaya of dharmakaya is Buddha Samantabhadra; the sambhogakaya of dharmakaya is Vajradhara; the nirmanakayas of dharmakaya are the 5 lords of the buddha-families. So, Amitabha, as head of the Lotus family, is classified here as nirmanakaya. The dharmakaya of sambhogakaya is Vajradhara; the sambhogakaya of sambhogakaya is Vairochana Gangchentso; the nirmanakaya of sambhogakaya is Sakyamuni Buddha. The dharmakaya of nirmanakaya is Amitabha; the sambhogakaya of nirmanakaya is Chenrezig; the nirmanakaya of nirmanakaya is Guru Rinpoche. So, here, Amitabha is the dharmakaya.
http://www.purifymind.com/Amitabha.html
In the works of ShanTao we see him arguing that Amida should be thought of as a Sambhogakaya. This gets carried over into the doctrines of Jodo Shu via Honen, which can be found here. However, I am not sure that ShanTao came to the same conclusion of Shakyamuni as Nirmanakaya and I'm not really sure how well referenced that statement is. I suggest tabling the question of Sambhogakaya Amida's Nirmanakaya form, or taking one of the answers in the quotes above rather than arguing this issue that may be somewhat controversial.
In the Larger Sukhavati Sutra, Amida Buddha is the culmination of Vows made by Dharmakara Bodhisattva. He is associated with the Pure Land of Sukhavati. He can be perceived by those with the right karmic connections to him. Thus, these facts seem to conform to our (somewhat tentative) definition of Sambhogakaya above. For what it's worth, this is probably where I fall in this issue. The Dharmakaya is completely unfathomable and the Sambhogakaya is how we can come to know the Dharmakaya if the right karmic conditions are present. Bodhisattvas can interact with Sambhogakaya Buddhas for help along the path to Buddhahood. Everyone can see and interact with a Nirmanakaya Buddha that is born into the world, but they are very rare and have limited life spans. As stated above, Sambhogakayas are without an end, but a start, which is much more in line with the descriptions in the Pure Land Sutras imho.
Amida as Dharmakaya
In the Kyogyoshinsho, Shinran quotes TanLuan in asserting that Amida is the Dharmakaya manifesting as compassionate means (as opposed to manifesting as Thusness). Rennyo makes similar assertions in his OFumi, but also sometimes falls back to the ShanTao position of Amida as Sambhogakaya.
As mentioned in one of the quotes above, Amida appears in the doctrine of the Five Dhyani Buddhas, which is used by Vajrayana, appears in the Shurangama Mantra from the Shurangama Sutra, and appears in certain iconography like the crown of some Chinese statues of Ksitigarbha. These 5 Buddhas represent aspects of the Dharmakaya, and Amida represents the Buddha's compassion (or the wisdom of observation).
The visualization of Amida in the Meditation Sutra really seems to be describing the Dharmakaya - manifesting countless Buddhas in his light which shines (unimpeded) throughout the Ten Directions. Meanwhile, the visualization of Avalokitesvara has him emanating countless Shakyamunis. I've always thought light that is infinite, shining unimpeded throughout the ten directions sounds an awful lot like some of the descriptions of the Dharmakaya. The passages in the larger sutra about the Buddhas illuminating each other's lands, sounds to me like mirror-like wisdom. The recollection & praise of Amida's qualities (according to the Amitabha Sutra) affords one to be thought of & protected by all Buddhas - which would make one wonder what it is that all Buddhas have in common.
Personally, I would rather think of the Dharmakaya as unfathomable, without marks; as the Maha PrajnaParamita Sutra says "the mark of the Dharmakaya is no mark". Assigning a name, or an ego, or an identity to the Dharmakaya seems to be opening the door to confusion.
...
Would love to hear peoples' thoughts.