It seems that gentiles are allowed to offer burnt sacrifices, and may do so anywhere in the world. They do not need the Temple. A Jew may even instruct a gentile on how to do this.
What is the purpose of a gentile offering a korban? That is, what does it actually do for them? Offering sacrifices doesn't seem to be commanded by the seven Noachide laws in the same way that Jews are ordered to bring sacrifices. Does a gentile's korban grant specific blessings or atone for specific sins, or is it purely something they can do if they feel like it?