You should always leave a burn uncovered so that the burn is allowed to heal properly.
Burns need air to health properly and when covered the burn does not get enough air so it takes longer for the burn to heal.
When the burn is allowed to breathe and get air the burn will heal much faster.
You should only keep a burn covered when you have clothing that is gonna rub up against the burn.
Otherwise let the burn breathe and it will heal much faster.
The same is true with wounds.
Wounds should also be allowed to breathe when possible as the air helps speed up the healing process.