OK....too much going on here. Let's break it into pieces:
1) You said there were shingles on the flat roof, but you talked about
spreading tar over something. Over what? Over the shingles? Is that how the
existing roof is set up? Tar over shingles??? When you said "tar", did you
mean "tar paper"?
2) It's generally not recommended to put more than 2 layers of shingles on a
roof, and some municipalities have regulations which prohibit roofers from
doing this. My understanding is that it's because of the extra weight, not
because the first layer will swell. I put a 2nd layer on my garage 15 years
ago, and there was no swelling.
3) Where a part of the roof meets another surface, like the wall of a higher
part of the house, or chimney and vents, you need to do various kinds of
creative and skillful artwork with bent shingles, flashing, and/or caulk. If
you do it wrong, you may still end up with leakage, if that's where the
problem is. If winter's upon you and you don't have time to do a little more
research into doing it right, you may, in fact, be better off having a
roofer do the whole job.