Favper- is a prefix that can be added onto any gender. It means that an individual feels a certain gender only when around that individual's favorite person (also known as an FP). Because of this connection, this term is exclusive to individuals with Borderline Personality Disorder, also known as BPD. 
Both favper- and borderix genders are experienced when one is away from one's favourite person. The difference between these terms is that a borderix individual's gender doesn't feel as intense and almost non-existent when without an FP, whereas a favper- individual does not feel their gender at all when away from their FP.
For example, someone who identifies as a favperman will only identify with being a man when around their FP.
Another example includes someone who primarily identifies as genderfaun, however when around one's FP, their gender feel more non-binary or even feminine. They might then identify as favpernonbinary or favperfem.
"Favper" is a portmanteau of "favorite" and "person". Favorite person is a term exclusive to those with Borderline Personality Disorder.
History and Flag
The term was coined by the Discord user Astronomical Chaos#8607 (handle may be outdated) - specifically by their system member Loki (part of the Astronomical Chaos Cluster) who wanted to describe his experience with gender while being with his FP.
The flag is supposed to be a combination of two different BPD flags and the non-binary flag, with the colors being more faded. The flag was made by the same user.