The Flurry of Blows class feature allows the character to spend 1 ki point to make two unarmed strikes as a bonus action.
Is this in addition to the bonus unarmed strike that monks get from their Martial Arts training (aka: for a total of 4 attacks - 1 regular attack, 1 bonus action unarmed attack, 2 bonus KI unarmed attacks) ... or is it in place of the Martial Arts bonus attack (1 regular attack, 2 bonus unarmed attacks)
Either the additional unarmed strike from Martial Arts or the two strikes granted by Flurry of Blows use a bonus action. (PHB p.78, variously)
But "you can take only one bonus action on your turn, so you must choose which bonus action to use when you have more than one available to you." (PHB p.189, "Bonus Actions")
You will have to choose one feature or the other, as they both consume your only bonus action. You will have either 3 attacks on your turn with the Martial Arts feature, or 4 (or 3 if you lack the Extra Attack feature) with Flurry of Blows.
Per the description of Flurry of Blows on PHB p. 78 (emphasis mine):
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.
Then, under the Martial Arts feature:
When you use the Attack action with an unarmed strike or a monk weapon on your turn, you can make one unarmed strike as a bonus action. For example, if you take the Attack action and attack with a quarterstaff, you can also make an unarmed strike as a bonus action, assuming you haven't already taken a bonus action this turn. (ibid., emphasis mine)
Since you only get one bonus action on your turn, you choose one or the other as indicated here on PHB p. 189, under the "Bonus Actions" heading:
You can take a bonus action only when a special ability, spell, or other feature of the game states that you can do something as a bonus action. You otherwise don’t have a bonus action to take. You can take only one bonus action on your turn, so you must choose which bonus action to use when you have more than one available.
