2 Questions.
Given that the rules say that the Flurry of Blows happens Immediately after the Attack Action.
1) Can the monk move between the Attack Action and the Bonus Action if you use Flurry of Blows?
2) Can the monk move between the unarmed strikes of the Flurry of Blows?
Strictly speaking no, and no... maybe

.
You can split your movement before and after your
action, so reasonably you could move, attack, finish move, bonus action.
1. However, since Flurry of Blows specifically states "
immediately after you you take the attack action,..." you cannot move first after the attack action. If you move, you are not using flurry of blows "immediately". If you take out the "immediately" key word, then yes you could. But it is there, so... no.
2. You can only split up movement between attacks granted by the action. Since the attack is granted by a
bonus action, you could argue no movement is allowed between the flurry of blows. Just the difference between an action and a bonus action. If you argue that the wording of
action includes a bonus action, then sure.
As a DM, I would rule no on both but it would hardly be a bad thing to rule the other way.