Killing an enemy adds a fly to the jar, up to a maximum of 20.
Upon use, releases Blue Flies equal to the number of flies in the jar.
This item belongs to the Beelzebub set. Collecting three items from this set will transform Isaac into a giant humanoid fly.
Notes
Kills by blue flies and locusts (including flies from the jar) and certain familiars (including Incubus and the launch attack from Tainted Lilith's fetus) do not add flies to the jar.
Friendly enemies such as from the Friendly Ball add flies to the jar, but not those spawned from other enemies.
Batteries do not affect the number of flies in the jar.
Enemies must be actually killed to add a fly; transformations (such as Gapers turning into Pacers) or knockouts (such as incapacitating a Globin) do not count as kills.
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.
Synergies
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.
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.
Interactions
Ace Cards: Enemies that are turned into pickups do not grant extra flies.
The item's pickup quote references the tagline of the Pokémon games. The quote said "Gotta catch 'em all?"
With Booster Pack #2, this item's sprite fills up with more flies depending on how many flies it contains. This is based on this Steam Workshop mod by Stewartisme.
The item is likely a reference to the Alice In Chains album of the same name.
Beelzebub set. Collecting three items from this set will transform Isaac into a giant humanoid fly.
Incubus and the launch attack from 
Tainted Lilith's fetus) do not add flies to the jar.
Friendly Ball add flies to the jar, but not those spawned from other enemies.
Gapers turning into 
Pacers) or knockouts (such as incapacitating a 
Globin) do not count as kills.
Shopkeeper will count as a kill.
Stone Grimaces will add flies to the jar.
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.
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.
Car Battery: No effect.
E. Coli/
Flush!: Enemies that are turned into poop do not grant extra flies.
Frozen enemies do grant extra flies.
Void: Flies will not collect when absorbed by Void, making the interaction worthless.
Infestation 2: Blue Spiders spawned by Infestation 2 grant extra flies, and Blue Flies spawned by Jar of Flies spawn Blue Spiders.
Bug!
The Ludovico Technique with 
Brimstone or 
Technology will not spawn flies.
Beelzebub 
The Binding of Isaac: Rebirth
