Unchained monk's flying kick and provoking AOOs

Actually:

 

Movement During a Charge

You must move before your attack, not after. You must move at least 10 feet (2 squares) and may move up to double your speed directly toward the designated opponent. If you move a distance equal to your speed or less, you can also draw a weapon during a charge attack if your base attack bonus is at least +1.

You must have a clear path toward the opponent, and nothing can hinder your movement (such as difficult terrain or obstacles). You must move to the closest space from which you can attack the opponent. If this space is occupied or otherwise blocked, you can’t charge. If any line from your starting space to the ending space passes through a square that blocks movement, slows movement, or contains a creature (even an ally), you can’t charge. Helpless creatures don’t stop a charge.

If you don’t have line of sight to the opponent at the start of your turn, you can’t charge that opponent

So yes, you need to charge in a straight line.

http://www.d20pfsrd.com/gamemastering/combat/#TOC-Standard-Actions

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