If shooting a flintlock I'll set off a little prime in the pan - blow down the barrel then pick the vent with a pipe cleaner after running a dry patch...
I don't see the use of priming the piece, except that it may burn some oil out of the vent. If that is what you are trying to do, then I suggest running a dry patch down the bore first. The air pressure in front of the patch should push oil out, after which lighting off a small prime may burn off any residual lubricant.
With a caplock, popping off a cap with the muzzle by a leaf or patch of grass provides enough pressure to push any oil out of the nipple and bolster and you should see the leaf/grass move. If you don't, pop off another cap or two; if there still isn't any movement of the light stuff it is time to clean out the nipple and fire channel.
At any rate, always run a dry patch down the bore first to remove oil. I have even gone so far as to run a patch moistened with isopropyl alcohol down to dissolve the oil and dry the barrel (a tip I read on the old MLML site) followed by a dry patch.
AS Rondo posted, I also blow down the bore after the shot and watch the smoke....
~Kees~