No. You don't declare actions separately from actually taking them.
I address a similar point in my answer here to "Initiative: Do I lose my attack/action if my target moves or dies before my turn in combat?".
Chapter 9 of the PHB/basic rules describes how actions in combat work.
It doesn't state anywhere in the "Combat Step-by-Step" sidebar in the "The Order of Combat" section, nor anywhere in the rest of the chapter, that you declare your actions before taking your turn.
In fact, nowhere in any of the rules does it state that you must declare the action you intend to take at any point; it only says that you take them (some at any time, some when a certain condition is met or when a feature/spell lets you take them). There's nothing in the rules that requires you to declare your actions beforehand - you simply do the things you want to do on your turn, if you have the movement, action, or bonus action (or whatever other resource it takes) available to do so.
In particular, the Flurry of Blows option for the monk's Ki feature says:
Immediately after you take the Attack action on your turn, you can spend 1 ki point to make two unarmed strikes as a bonus action.
This means you take the Attack action in full, then spend a ki point to make those 2 unarmed strikes as a bonus action. In particular, when you use Flurry of Blows, at least the first unarmed strike happens immediately - you don't use Flurry of Blows without at least starting to do the thing that Flurry of Blows is.
That said, the rule on moving between attacks states:
If you take an action that includes more than one weapon attack, you can break up your movement even further by moving between those attacks. For example, a fighter who can make two attacks with the Extra Attack feature and who has a speed of 25 feet could move 10 feet, make an attack, move 15 feet, and then attack again.
A bonus action is a type of action, and Flurry of Blows consists of more than one weapon attack (as unarmed strikes are "melee weapon attacks" despite not being made with weapons). Thus, you can move between the attacks of Flurry of Blows... But you still can't move after using Flurry of Blows but before attacking, because using Flurry of Blows entails making an attack as part of it, in the same way that using the Attack action entails making an attack as part of it.
Rules designer Jeremy Crawford unofficially confirmed this interpretation of the rules in this May 2018 tweet:
D&D combat is sequential, with no action-declaration phase at the beginning. Your turn can also be interrupted by someone’s reaction. Such an interruption could, among other things, incapacitate you, meaning your intention to take a certain action was never fulfilled.
He reiterated that sentiment in a later tweet from the same month:
D&D combat doesn't have an action-declaration phase. Things happen in order, and you can be interrupted at any moment by a reaction, trap, or the like. You can say, "I plan to take the Attack action," but that has no rules relevance until you're actually taking the action.
Crawford specifically addressed the case of Flurry of Blows in this March 2019 tweet, though he was talking about needing to actually take the Attack action first to qualify for Flurry of Blows:
In D&D, the way you take an action in combat is to actually take the action. There is no action-declaration phase. Flurry of Blows happens after the Attack action, which means the action itself, not a declaration that you will take the action.
Even though this tweet doesn't directly address your question, rider effects on Flurry of Blows obey a similar logic. You can't use Flurry of Blows without making one of the unarmed strikes that Flurry of Blows lets you make - there's no "declare that I'm using Flurry of Blows" step to the process. Once you start using Flurry of Blows by making your first unarmed strike as part of it, then you can move before you make the other unarmed strike that's part of it.
