You are making a decision between the 3200 and 5100. You might want to check out one of the later additions to the "D5100 or D5200?" thread. In it, the poster mentions a blog where he compares a 5100 with a 5200. Since the 3200 seems to have a "better" sensor than the 5100, there may be other things better as well. He mentions a number of things that I have never seen discussed here. So you might want to make a note of these things and then do a comparison of the 3200 and 5100 based on these things. The 3200 might actually be a better choice than the 5100 even without considering any price difference.
As far as kit lenses go, the 18-55 that I got with my 5100 is a very nice lens. Some kits come with more than one lens.
What kind of birds do you want to shoot? Geese, hawks, eagles etc that are some distance away or small birds that are perched or flying. I use a 5100 with a Sigma 150-500 to shoot small birds flying toward a feeder. For this I zone focus and run the camera on full auto. There have been a number of times in which the bird's head was coming into the frame in one pic and his tail is flying out of the frame in the next pic. I understand the 3200 has a 5 fps rate while the 5100 has only 4 fps. That might make a difference in that situation. Also, with the higher pixel density of the 3200, you might be able to get away with a smaller lens and then crop tighter to get the same picture.