With Greater Grappling, which allows me to maintain a grapple with a move action instead of a standard action, would I be able to perform a flurry of blows? With flurry of blows, as a full attack action, I can take a 5 foot step which is a move action. If I did not take this 5-foot step I was thinking this would count as the feat's move action requirement for maintaining the grapple and allow me to perform my flurry of blows.
Thanks!
No.
If you use a move action to maintain the grapple, you can take a standard action but not a full-round action. A full attack requires a full-round action, so it's out.
A 5-foot step is a free action and not a move action. You can't "use" a five foot step to do anything else; it's just changing your position by one square. That's it.
5 ft step is not a move action. It is a free action. see the combat section for what type of action things are.
You cannot perform a move action and a full round action in the same turn, so no, you cannot use flurry of blows with greater grapple.