The gemara says that the fact that milk of a kosher animal is permitted to drink is a chiddush because one could have argued that it would be included in either the prohibition against blood (דם נעכר ונעשה חלב), or the prohibition against אבר מן החי since it is part of a live animal. The gemara cites three possible pesukim as the source of the fact that milk is kosher (either the pasuk when Dovid brought milk to the troops, or the pasuk that praises the land of Israel for it's milk which indicates that it is permitted to drink, or a pasuk in Yeshaya).
The Shita Mikubetzes asks, why not use the pasuk by Avrohom when he fed the angels butter and milk. Being that Avrohom kept the entire Torah, the fact that he was willing to give milk to the angels indicates that it is permitted to drink? The R"I answers that Avrohom thought that they were bnei noach. Even if milk were forbidden to Jews, it wouldn't be one of the 7 Noachide laws and permissible for them to drink it. The Shita then cites a Yerushalmi (which is not in the Yerushalmi but in the pesikta and quoted by the da'as zekeinim on parshas vayera) that indicates they ate meat and milk (unlike the gemara in baba meztia which implies that didn't actually eat, and also says that it was served one by one i.e. milk before meat) . When it came time to give the Torah and the mal'achim were complaining they wanted to keep it, Hashem said that every child knows that meat and milk can't be eaten together, yet they ate meat and milk when they visited Avrohom. It isn't clear how this midrash connects to the discussion of the Shita Mikubetzes. Perhaps the Shita is trying to prove that Avrohom thought they were bnei noach from the fact that he fed them meat and milk, so there wouldn't be any proof from there about milk being permitted to drink.
The Maharit Algazi asks that according to the rationale that milk would be assur as אבר מן החי, it would surely apply to non-jews as well. The answer of the Shita that Avrohom assumed they were bnei noach doesn't work if the issur on milk would be an offshoot of אבר מן החי? The Chasam Sofer (y.d. 70) answers that the gemara never really suggested that milk would actually be אבר מן החי or בשר מן החי because it is neither an ei'ver or ba'ssar. Rather the gemara was suggesting that it should be LIKE אבר מן החי in the sense that it would be assur (not not for goyim), based on concept of הטמאים - לאסור צירן ורוטבן וקיפה שלהן. Meaning, since אבר מן החי is assur and the animal is assur when it is alive, so anything that comes from it when it is alive should be included in the prohibition of הטמאים. This prohibition would certainly apply to Jews only, therefore Avrohom would have had no problem giving milk to b'nei noach.