I think this is a non issue and not worth worrying about. By the time you burn out a barrel shooting semi-auto, the cost of replacing the barrel is going to be a drop in the bucket compared to the cost of the ammo that it took to burn the barrel out.
If you are just asking for the sake of curiosity, it's hard to answer your question. The number of rounds fired must be considered in light of the manner in which they were fired. Doing repeated mag dumps will accelerate the wear on the barrel.
Still, just as a point of reference, my beater carbine with a plain ole Bushmaster chromelined barrel has over 10K rounds through it and it still shot MOA or so with good ammunition the last time I pulled the ACOG off of it and used a bigger scope to see what it would do. I rarely do mag dumps, but do shoot it fast when I work on multiple target practice.