Mishnayos maseches Kinim can be reduced to a few rules. I think they're as follows (though it's been a while, so I may be messing some of these up).
- A bird ola is brought on the top of the mizbeach, and chatas on the bottom. Do either one wrong, and it's invalid.
- A chova is one chatas and one ola; a neder or n'dava is two olos. If you bring more olos or chataos than that from a ken, the excess are invalid.
- Both birds of a ken are b'ne yona, or both torim. If a mixed ken was brought, only the chatas is valid; ben Azay says only the first brought is.
- If a bird may have been designated as a chatas, it cannot be brought as an ola; and vice versa.
- If a bird can't be brought or was brought but is invalid, bring a new one in its stead, and its former mate is fine.
Why, then, does the maseches go on and on with examples instead of simply stating the rules? Mishnayos, from what I understand, are usually written to be easy to memorize. Surely Kinim as we have it is harder to memorize than the above.