Achillean (also known as Men Loving Men (MLM), Apollian, Chaeronean, and Chaeronic) refers to a man who is attracted to other men. This term is also sometimes used by non-binary people. This attraction doesn't have to be exclusive, as the label is used in a way to unify all men who love other men such as gay (vincian) men, bisexual men, pansexual men, etc, promoting solidarity among men of all identities. Since achillean is an umbrella term, it is typically not used as an identity on it's own, however it can be if desired.
The word achillean has historically been used to describe things relating to Achilles. The first instance of achillean being used in the context of MLM is likely a 2016 post by Tumblr user Asculan.
The achillean flag has two blue stripes on the top and bottom representing men. In the center is a green carnation. In ancient Rome and 19th century England green indicated gay affiliations. Victorian men would often pin a green carnation on their lapel as popularized by author Oscar Wilde.
An alternative flag uses a darker blue with a green stripe alongside the green carnation, with the same symbolism.
The original achillean flag had the same two blue stripes on the top and bottom representing men as the current flag. In the center was a realistic green carnation, but this flag was too complicated for many and could not easily be made in vector formats, leading to the creation of the current flag.
The word achillean comes from the name of the hero in the Iliad, Achilles, who was romantically involved with another man, Patroclus.