My conclusion goes like this:
- You can target each of your attacks against any target you choose that is valid at the moment you make that attack. Nowhere in the rules exist any restrictions regarding that.
- You can move between the Attack action and either the Martial Arts bonus action or the Flurry of Blows bonus action, and
- you can move between the two Flurry of Blows attacks too.
My reasoning for the latter two is the following: The flip side of Specific Beats General is General Applies Unless There's Specific. Basic Rules state that the general case is that you can split your movement before, after and between your actions; that is: you could move > bonus action > move > action > move, or viceversa, or any combination.
A specific subset of that is having two or more attacks in the same action (e.g. Multiple Attacks or Eldritch Blast); Basic Rules state the general case for this is that you can also split your movement between attacks within the same action too.
The text for Flurry of Blows, as written, doesn't mention movement at all and therefore doesn't add any Specific case, thus the General rule above mentioned would apply. The only possible point of contention would be the "immediately after you take the Attack action" part, which could be interpreted either as being meant to apply only to the trigger, or as starting the bonus action immediately. I think that the former adds less "moving parts" to the rules, so Occam probably favours that one; but even if the latter is correct we already can use our Movement within an action with attacks, so it isn't any stretch to think that RAW probably allows using move after declaring your bonus action but before making a Flurry attack itself.
This is softer evidence but it's still worth mentioning: Mike Mearls has stated (twice) that the monk can move "in between his additional unarmed attacks or his Flurry of Blows". Mearls may not be the "Official Rules Expert" so his words aren't as binding (FWIW) as the 5E designer's, but it's still interesting insight on what Rules As Intended are likely to be.