510.4.

A permanent retains its status until a spell, ability, or game action changes it, even if that status is not relevant to it.

Example: Dimir Doppelganger says "{1}{U}{B}: Remove target creature card in a graveyard from the game. Dimir Doppelganger becomes a copy of that card and gains this ability." It becomes a copy of Jushi Apprentice, a flip card. Through use of Jushi Apprentice's ability, this creature flips, making it a copy of Tomoya the Revealer with the Dimir Doppelganger ability. If this permanent then becomes a copy of Grizzly Bears, it will retain its flipped status even though that has no relevance to Grizzly Bears. If its copy ability is activated again, this time targeting a Nezumi Shortfang card (another flip card), this permanent's flipped status means it will have the characteristics of Stabwhisker the Odious (the flipped version of Nezumi Shortfang) with the Dimir Doppelganger ability.