I have used flash occasionally, with a Better Beamer and my 100-400. There is a good writeup here:
The problems I find are that I tend to use it too late - by the time I think it's "dark" enough for flash, it's really too dark, so flash becomes the primary illumination - and "steel eye", the avian version of "red eye". I really need to get out and practice with it more.
Same experience here. Definitely a learning curve I'm still climbing with that set-up. Lately I've started out with -1 1/3 or -1 2/3 EV flash exposure compensation around dusk or when in deep shade to fill in shadows without blowing out the overall exposure, but I still don't feel I've mastered long-distance flash. And eye reflection angle is definitely the detail to watch - catch-light is important, but steel eye/red eye is worse than no catch-light IMO.