How do flaming weapons work?

I recently made a level 8 Storm Herald Barbarian (from XgtE) with the Desert aura. The level 6 feature allows me to set flammable objects that are not being carried or worn by anyone else on fire. So my question is this. If I set a quarterstaff completely on fire, how much extra fire damage would it deal to my opponent, how much to me, and how long would it last before burning?