Perioriented refers to someone whose sexual orientation and romantic orientation have "matching" prefixes. For example, someone who is bisexual and biromantic, or someone who is gay (homosexual) and homoromantic are both examples of perioriented individuals. The noun form is periorientation.
Most perioriented individuals do not specify their romantic orientation, because one's romantic orientation can be assumed to be the same as sexual orientation unless specified otherwise. The sole common exception to this is aromantic asexuals (aroaces), as they are perioriented but do specify both orientations.
The opposite of perioriented is varioriented.
The history of the term is unknown. The flag was presumably created on Tumblr blog beyond-mogai-pride-flags on January 28, 2018 and has no known meaning.