I just flat crowned my barrel and I can detect just a very very slight amount of burring/sharpness with a Q Tip just at the extreme outer edge. What is the best procedure one could use to break this edge while still keeping everything concentric with the bore.
Is it catching lint off the Q-tip or does it just feel sharp? If it is collecting lint, recut the finish cut with a very sharp HSS bit and cut from the inside out with a fine feedrate.
If it just feels sharp, while it is still in the lathe use the shank of a Q-tip and with the lathe running forward, hold the Q-tip shank at about 45 degrees and "burnish" the edge slightly. Then reverse the spindle and do the same.
If you have a burr of even 0.005" or so and you shoot the barrel, and a piece breaks off, that barrel will not be as accurate as is normally would be.
Some gunsmiths, mostly folks who build hunting rifles use a round head brass screw and lapping compound to remove that sharp edge.
OR, probably the best, with the barrel indicated in the lathe to ZERO runout (as near zero and you can read on the indicator) cut a 45 degree bevel on that right-angle edge. In doing this indicate the grooves, then cut the bevel to where it is just barely past the grooves. This will be about 0.005". This makes a crown that is accurate and less subject to damage than a sharp edge.
If you try to cut a crown with a carbide insert you will probably will end up with some burr. There are only a very few carbide insert edges that are sharp enough to cut a burr free crown. Most carbide inserts have a small radius on the edge and that IMO does not make a burr free crown edge.