My kitchen sink was draining slowly and by process of elimination I concluded it must be the aav.as I removed the old one the drain started working properly.I replaced it with a new one and it worked normal for a day and then the sink started backing up again and draining really slow.it looks as if water is leaking either from the vent or where its threaded but the old one was only hand tightened as well.did I install it incorrectly? Is there more to just screwing it on?

When you installed the AAV did you use Teflon Tape on the threads? Dip the water out of the sink. Take a bucket and unscrew the AAV. If there's standing water in the pipe you have a blockage. Send a snake down the open pipe until all the water drains out;. Replace the AAV using Teflon Tape on the threads. Good luck, Tom

No I didn't use teflon tape but the old one didn't have any either,it wasn't on very tight just by hand.the problem is that the water backs up but still drains very slowly and I don't know why.as previously mentioned the water drained fine when I removed the old one and worked for about day with the new one.I can't figure why the problem returned seemingly worse.

My advice still stands,
Dip the water out of the sink. Take a bucket and unscrew the AAV. If there's standing water in the pipe you have a blockage. Send a snake down the open pipe until all the water drains out;. Replace the AAV using Teflon Tape on the threads.
Good luck, Tom

It sounds like you have a partial blockage in the drain line the solution would be to remove the "J" bend from the trap and send a snake up into the wall, (see image) You will hit a bend about 8 inches in but once around that you only have to put out 5 feet more. After, flush with a tub of hot water. If there is no blockage it shouldn’t leak from the AAV, good luck.

John