Recently I saw a youtube video describing what various gun tools were used for. The presenter said that the vent pick was used to occasionally clean out the vent in the barrel. This is not strictly true. It would be more correct to say that the vent pick is used to CLEAR the vent.
The vent rarely needs cleaning in between normal barrel washing chores. The vent pick is used to make sure that the vent is clear of gunpowder. The flash from the pan of the flint lock has to pass through the vent to reach the main charge in the barrel. If there is gunpowder blocking the vent, the flash from the pan has to first burn through the gunpowder in the vent. This can delay the ignition time, not by much, but it will delay ignition of the main charge.
Another precaution against a blocked vent is to insert a vent quill in the vent when loading, this will keep the vent clear.
The vent quill is also used to mark or signal a loaded gun even though the pan is not primed. This is to avoid any chance of double charging. The vent quill is left long enough that it can clearly be seen sticking out of the lock.The vent pick can be fancy, or it can be a piece of wire bent to shape. Both work equally well.
The brush on the left is a bought one. The brush on the right is mine, and I made it from horse hair bound with linen thread.
The pan brush is used to clean the pan of any gunpowder residue. If you have the time, this should be done between shots, especially on damp days. The potassium nitrate in the gunpowder attracts moisture so you need to clean the pan well. After using the pan brush I often wipe the pan out with a piece of cloth if the weather is wet.