Long ago, when I didn't know better, I used to blow down the barrel to put out the embers before reloading, just because everyone else at my club did it that way. Then I got smart.
I now- and have for more than 25 years- run a cleaning patch down the barrel after every shot wetted with spit. This softens the crud, removes some of it, and absolute puts out all embers. I always watch my touch hole, or nipples to see if smoke is coming out, so I know the path is clear for the next shot, and by judging the density of any smoke that does come out, I know if its just smoke from the prior shot that remains in the barrel, or " new " smoke from actual burning embers. My experience is that when shooting a proper load, with the correct ball and patch combination, or when using a filler to seal the gases behind the ball, that I get far better and more complete burning of the powder, and almost never have a burning ember in the barrel. However, even though this is a rare event, I still use the damp cleaning patch down the barrel to put out the embers. It does require me to run the ramrod down between shots, but I am not in a hurry when I shoot BP, and there is no excuse for risking your own and someone else's safety by cutting corners.