No. The Attack action is a specific action that you take in combat, which can include multiple attacks. From page 71 of the Player's Basic Rules:
The most common action to take in combat is the Attack
action, whether you are swinging a sword, firing an
arrow from a bow, or brawling with your fists.
With this action, you make one melee or ranged
attack. See the “Making an Attack” section for the rules
that govern attacks.
Certain features, such as the Extra Attack feature
of the fighter, allow you to make more than one attack
with this action.
The important distinction to understand here is the difference between "the Attack action" and "an attack". Flurry of Blows can be used after you take the Attack action, not after an attack.
So you take the Attack action, using Extra Attack to attack twice, then you can spend a ki point and use your bonus action to attack twice with Flurry of Blows.
It should be noted that even if Flurry of Blows could be used after an attack rather than after the Attack action, it still requires a bonus action to use, and you can only use one bonus action per turn.