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 people.
Most perioriented people 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 exception to this is strictly aromantic asexual (aroace) people, 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. The flag has no known meaning.