I have a swarm-summoner in a level 15-15-14-13 party that I'm DMing in. He has explained to me that swarms may join together to increase their hit dice, damage, saves, size, etc. I was wondering if this is really the case and if he were to benefit greatly by becoming a swarm via his Master of Flies class ability and joining his summoned swarms.
I don't see any rule that allows swarms to merge and also
Without some form of outside mind control, swarms attack all creatures in their cell
This includes other swarms
From Summon Swarm
You summon a swarm of bats, rats, or spiders (your choice), which attacks all other creatures within its area. (You may summon the swarm so that it shares the area of other creatures.) If no living creatures are within its area, the swarm attacks or pursues the nearest creature as best it can. The caster has no control over its target or direction of travel.
Emphasis mine. Most if not all swarm summoning should have similar language, mindlessness is a trait of Swarms.
No, swarms summoned by a character remain separate swarms, they do not merge to form a larger single swarm unless the spell or ability description says so explicitly.
Possibly the confusion comes from these words in the Swarm subtype description:
Larger swarms are represented by multiples of single swarms. The area occupied by a large swarm is completely shapeable, though the swarm usually remains in contiguous squares.
Note that though the text speaks of a single large swarm, it is stated that the large swarm is represented by multiples of single swarms. That is mechanically they remain single swarms and all their characteristics including HP should be tracked separately.
There is no rule allowing swarms to merge.
Multiple swarms are treated separately, not as one.
[...] Larger swarms are represented by multiples of single swarms. The area occupied by a large swarm is completely shapeable, though the swarm usually remains in contiguous squares.