Whether pellets work in a flintlock depends on which flintlock your talking about.
The flintlock guns that have a vent hole that goes directly thru the wall of the barrel into the bore can only use pellets if you do like SDSmlf described and even then it will only work if the initial amount of real black powder is higher than the distance from the breech plug face to the vent hole.
The reason for this is, if the black powder is not taller, only the side of the pellet will be exposed to the flash and the heat from the powder flash in the pan is not enough to light the synthetic powder the pellet is made from.
The people who make those pellets know that even the flash from a percussion cap won't ignite a pellet if it is made using just the synthetic powder. That's why pellets have a layer of real black powder, mixed with a binder on one or both ends of the pellet.
Thompson Center made one model of their flintlock Hawken rifles that were supposed to work with pellets. I guess they work sometimes but I read quite a few comments by people who owned them that indicated they weren't very reliable if only pellets were used.
These TC guns had a special breech plug that was supposed to guide the pan flash in the pan directly to the black powder base on the pellet.
This said, the only reason I can think of for using pellets is the speed that they can be loaded into the barrel.
On the negative side of using pellets, they cost a fortune compared with loose black powder. They also restrict the powder to one or two amounts of powder which is not conductive to good accuracy. (Usually, the most accurate shots from a muzzleloader will be a very different amount of powder than the 50 or 100 grain pellet sizes). For instance, my .50's shoot best with a 70 grain powder load and my .54's shoot best with a 80 grain powder load. (Yes, these are good for hunting deer.)