With items that kill normally unkillable enemies, killing things like Stone Grimaces will add flies to the jar.
Killing minions in the Hush fight does not add flies to the jar.
Fish Tail: Doubles the number of flies that spawn.
Hive Mind: Flies are bigger and deal double damage.
Schoolbag: Flies will be gained even while the Jar of Flies is in the inactive slot.
Book of Virtues: Using Jar of Flies summons wisps instead of Blue Flies; the wisps do not summon the flies when destroyed. Up to five flies at a time are consumed to summon one wisp, with stacking health and damage. The damage of the wisps decreases as they take damage. Enemies killed by wisps’ tears will not add flies to the jar.