So far a health regen (and fade away) Fl4k with the Bff skill (gives allies a percentage of Fl4k’s health regen), and a melee Amara using her health regen passive is working decently with the right gear for each character.
My Fl4k is doing plenty of damage with his crit weapons, while all that added health regen is keeping my friend’s melee Amara alive and I can either use fade away for the increased crit, as an escape plan, or to cloak and revive my allies.
However looking at the skill trees I think they could all possibly synergize fine if played by co-op capable people. Of course this is just my opinion based on what I have seen so far given that I have only played as Fl4k so far. Also even though I was in a full group with all 4 characters for a couple hours, Zane and Moze were specced for solo play by friends that prefer to rush around doing their own thing and not being that co-op capable.