We know that of the Dashavataras, Lord Krishna was the most divine and poorna avatara of Lord Vishnu while Lord Rama's divinity is questioned. But what about Lord Kalki? Will He be aware of his divinity?
Yes. Lord Kalki will be aware of His divinity. Like Sri Krishna, Lord Kalki will also take birth with four arms and upon request, He assumes two armed form. Here's how Chapter 2 of Kalki Purana describes this event (translated by Bhumipati Das)
18-19. Lord Brahma, who knew the mystery of the Lord's appearance, hastily called for his servant, Pavana, and told him to immediately go to the maternity home and offer the following prayer to Lord Visnu: О Lord, please consider how this four-armed form of Yours is rarely seen, even by the demigods. Please assume a two-armed form like that of a human being and then carry out Your mission.
Without delay, Pavana-deva, whose cooling body has a very pleasing aroma, went to the maternity room of Lord Kalki and submitted Brahma'.s appeal.
When the lotus-eyed Lord heard this request, He immediately assumed a two-armed form. His father and mother were certainly struck with wonder upon seeing this wonderful pastime of the Lord.
This clearly shows Lord Kalki will be aware of His divinity, like Krishna.
Also, in Chapter 3, His guru Parasurama says He is Lord Vishnu.
- Parasurama said: О great soul! Long ago, Brahma prayed to Lord Visnu, the shelter of all living entities and the Supreme Personality of Godhead, to destroy the influence of Kali. I understand that You are that same Supreme Personality, appearing in the village of Sambhala
There are many other incidents in kalki Purana which say Kalki will be aware of His divinity.