"If you are a bird I am a bird" VS "If you were a bird I ...." which is right?

"Are" is a present-tense form of the verb to be. So saying "If you are a bird..." is an observation about what a person is now:

If you are a bird then I must be a bird.

Although nonsensical, it is following the logic that you and the other person are the same, so if the other person is something, you must be the same.

"Were" is a past-tense form of the verb to be, however, it is also used to hypothesize about something that might happen. This usage is normally recognisable by the conditional "if".

You might say:

If I were a bird I would fly away.

This is a purely whimsical statement - saying that if you were a bird, hypothetically you would fly away. There is no logic here.

This doesn't really work with your example statement, because it cannot be "logical":

If I were a bird, then you would be a bird.

Your hypothetically being a bird does not dictate that someone else would be one too. I think for this example you need "If you are....".

Your other example though is not about logic:

"If you were a bird I will kill you"

This is entirely hypothetical because it is about what you would do if another condition was met (the other person was a bird). The only thing wrong with this example is that, when speaking about a hypothetical future, "will" should be "would":

If you were a bird I would kill you.