Pap,

I cook marinated leg quarters all the time on a Weber kettle grill. Key to preventing flare-ups is to cut off the O2 source until the fat burns off. I put the cover on and close it down for a few minutes till things calm down.
Been doing it a long time and it always comes out great. Skin is nicely browned but not burned. Baste the last 10 minutes for best results.