I've flared case mouths for cast bullets, but can't recall ever needing any more than a good chamfer on case mouths for jacketed. It may be the solution here though.
The main point I wanted to make is that if you do flare them, you may notice that you need to anneal case necks, or at least case mouths, a bit more often, to avoid getting little short cracks right at the mouth of the case, from the additional cold working.
