I do not have the precise location but I was taught that the Yalkut Yoseph brings down eight answers/considerations to this question. Here are some highlights:
According to Rashi the milk was served first which is entirely permissable. According to the Maharal, Avraham only fulfilled the positive commandments while the Gra brings opinions that he wasn't particular regarding Rabbinic commandments (there is no indication the meat and dairy where cooked together which would constitute a Torah prohibition). And regardless of his own observance, the Shita Mekubetzus points out he thought they were b'nei Noach [non-Jews who are not obligated to separate meat and dairy].
Of course this was before the Torah was given so the question doesn't really begin if one takes a minimalist approach to the question of whether the Avos kept the mitzvos.