This is, unfortunately, one of those times when the poor grasp of the English language causes problems.
I am aware of who said it, but it's explicitly stated that "you can attack twice, instead of once, when you take the Attack action on your turn." Now this states you take the attack action before using up all of your attacks because otherwise you are incapable of attacking when you take the action. It also suggests you have taken the action before completing it, so then we'd be in the realm of "immediately after" instead of it saying "upon completion of an attack action."
Again, while I do enjoy the slight roughshod flexibility of 5th edition with so much interpretation even the creator of the game disagrees with what he put in text, because the person responsible for ensuring Extra Attack, Section 8's combat text and the Monk ability Flurry of Blows was not employed to actually perform a check that they all make sense together.
As such you should feel free 100% to allow the Monk to flurry of blows after either attack and if anyone questions it, give them a stern look like you're about to deduct XP or throw them in a pit of acid they cannot escape out of. (But don't let him use more than 1 Bonus Action unless you want him to be super powerful!)
I am aware of who said it, but it's explicitly stated that "you can attack twice, instead of once, when you take the Attack action on your turn." Now this states you take the attack action before using up all of your attacks because otherwise you are incapable of attacking when you take the action. It also suggests you have taken the action before completing it, so then we'd be in the realm of "immediately after" instead of it saying "upon completion of an attack action."
Again, while I do enjoy the slight roughshod flexibility of 5th edition with so much interpretation even the creator of the game disagrees with what he put in text, because the person responsible for ensuring Extra Attack, Section 8's combat text and the Monk ability Flurry of Blows was not employed to actually perform a check that they all make sense together.
As such you should feel free 100% to allow the Monk to flurry of blows after either attack and if anyone questions it, give them a stern look like you're about to deduct XP or throw them in a pit of acid they cannot escape out of. (But don't let him use more than 1 Bonus Action unless you want him to be super powerful!)