The Rambam and the Rashba in Chullin 129b suggest that the prohibition for a ben Noach not to eat basar min hachai differs from that of a Jew’s. While a Jew is prohibited as the meat is considered traifa, a ben Noach is prohibited because of the pasuk in Parshas Noach: “ach basar bnafsho damo lo sochelu”(9:4).
Adam Harishon was not allowed to eat meat. It would have been considered stealing if he would eat the meat since Hashem did not allow him to eat that. After the mabul Hashem permitted Noach to eat meat, but added “ach basar bnafsho damo lo sochelu” – that one may not eat the flesh with its soul. The Gemara explains that this is a reference to eiver min hachai. Some acharonim explain that while it became permitted to kill an animal and eat it, eating in a forbidden manner was never permitted and is still prohibited from the time of Adam Harishon.
Therefore even if milk were forbidden as eiver min hachai, nevertheless for a ben Noach it may have been permitted since that it something that people were permitted to use. However, for bnei Yisrael, if the prohibition to consume milk was because it was eiver min hachai just because it was intended for human consumption would not permit it. Therefore, the Gemara in Bechoros could not cite the pasuk by Avraham Avinu as a source the milk may be consumed by bnei Yisrael.