[KenProspero]

First, the odds of you getting KK are 1 in 221.
The odds of a specific other player getting AA after you get KK are a little better than 204 to 1, since there are 5 other players in the game, the odds of one of them having AA (with you not having an A) are a little less than 1 in 41.

So, you'll be up against AA roughly once in 41 times that you have KK.

Before a hand starts, the odds of YOU having KK and someone else having AA in a six handed game is roughly 1 in 9026.

Now, onto your question. The odds of anyone having KK and Being up against AA is roughly 1 in 1504. (chances of any one individual having KK is a bit less 1 in 37 (221/6). As already stated, given the existence of a KK holding, the odds of an AA holding are about 1 in 41. Multiply 41 by 37, and you get 1517 (however, without the rounding, it comes closer to 1504).

This is back of the envelop but it should be close enough.