Marvin, like you, I use the chuck to do the flare. But like you said, I round the blank between centers first and make sure the end is square. That makes it real easy to mount in the chuck. After drilling, I do like you, and use a tool to flare. Sometimes I start with a step drill, just to speed up the process. Takes a bit less turning that way. Like you said though, don't get too aggressive. That blank flying out of that chuck is not a fun experience. Been there, done that. :(
If I am doing a closed reed call, I will drill part way with a 5/8" drill, and the rest with a 1/4" drill. Then I do the flare. I then mount it on a pen mandrel, with a turned insert for the taper mounted on the pen mandrel, and finish turning the call. Like you said, there is more than one way to skin this cat, just what ever works is the way to go.
Edited for major grammatical and spelling errors. >:(