I fail at the search option, as it brought me zero results when searching for flank or engaged.

Assumption - There are no engagement markers on the table.

-Situation - Lannister Unit meelee unit attacks Stark unit - Does zero wounds, and no retreats - I place a Lannister Engagement unit between them.

My Quesno - Stark players turn - If they attack the Lannister unit that is now engaged with the stark unit, do they gain the flank bonus against that Lannister unit?.(even though its a lannister engagement token) The ruleback says if a unit is engaged, they get to be flanked. It doesnt say it has to be a Friendly engagment token..

Do you need to be flanking a unit that is in combat with a "friendly engagement token" to count as flanking? or just any engagement token?

It makes no difference which engagement token it is. Any unit that attacks a unit that is 'engaged' with another unit, gains flanking advantage. Of course, if the 2 units 'engaged' attack each other, then it is a normal attack. In fact, if they attack another unit or move away (apart from retreats) they get counterattacked. The only difference that the faction of the engagement token makes is in combat in building hexes. Cheers!