My kitchen sink drain seems to be flowing freely however, after the water has drained from the sink there is an annoying sound... ploop ploop ploop ploop ploop... for about 2-3 minutes. The drain wa snaked but the noise persists. Any ideas? Thank you.

Welcome to the club. Ours does the same. The only thing I can think of the reason for it is, inside the J trap,there are little things that stick out . Like shelves. Mine has those inside,and I just repiped the whole under sink plumbing and used a brass J trap. I am not sure of why those are inside because you would think they would cause it to clog up, but ever since I put the brass one in ,it makes that sound. That or the drain pipes are getting air inside and that is the reason. I don't know,I just know the sink is draining good now, so I am keeping quite about it. I don't want to jinx it!

Problem in not in your under-sink drains. It is past it. Your sink drain is grasping for air. It is either that your sink is not vented properly and / or your drain is still partially clogged.

Milo nailed it. The sound you hear is the sink venting through the trap. You both have blocked vents. The solution would be to snake the kitchen vent from the roof. Put out enough cable to reach the base and 20 feet more. Good luck, Tom