How to replace the flange from a tail piece of kitchen sink drain

I'm guessing you're going to have to replace the entire piece. The T junction your tail piece goes into appears to be welded in on the opposite side; I can't see the joint on your tail piece well enough to tell, but one would naturally assume if one side is welded, then the other would be too. If you can get a higher angle that shows the joint in detail we may be able to confirm that.

Given that premise, then my guess is you're going to have to either replace the entire piece or get someone to weld a new tail piece on. Unfortunately, I strongly suspect that it won't be possible to just replace the tailpiece in that T junction and you'll probably end up having to rebuild the whole thing. You can probably easily do it yourself with plastic parts and it should be doable using standard metal parts as well. If you want an exact replacement you'll have to have someone weld up that T junction and the dishwasher drain hose out of copper.

In order to disassemble your pipe, you should start with the J trap. Unscrew that and remove it (make sure you have a pan underneath; there'll be water in it), then disconnect the dishwasher hose. Next unscrew the pipe coming in horizontally from the other side of the sink, and once that's free you can take off the leaking connector and the part should be free.

The connection @jayeff is referring to is the threaded one marked in green; that should unscrew first, but in order to rotate the entire tailpiece you'll obviously have to disconnect the dishwasher drain hose too, also marked in green.

My suggestion was to undo the two threads at the bottom, marked in orange, to remove the J trap. Next, take off the two green ones as suggested, and finally you should be able to unscrew the blue one, either by itself or by rotating the entire assembly.