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You will have to choose one feature or the other as they both consume your only bonus action. You will have either 3 attacks with the Martial Arts feature or 4 (or 3 if you lack the Extra Attack feature) with Flurry of Blows.

PHB P78, emphasis mine:

Flurry of Blows. 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 Martial Arts:

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 in your turn you choose one or the other as indicated here PHB p 189 under Bonus Actions:

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.

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.

You will have to choose one feature or the other as they both consume your only bonus action. You will have either 3 attacks with the Martial Arts feature or 4 with Flurry of Blows.

PHB P78, emphasis mine:

Flurry of Blows. 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 Martial Arts:

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 in your turn you choose one or the other as indicated here PHB p 189 under Bonus Actions:

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.

You will have to choose one feature or the other as they both consume your only bonus action. You will have either 3 attacks with the Martial Arts feature or 4 (or 3 if you lack the Extra Attack feature) with Flurry of Blows.

PHB P78, emphasis mine:

Flurry of Blows. 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 Martial Arts:

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 in your turn you choose one or the other as indicated here PHB p 189 under Bonus Actions:

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.

Total of three as both options utilize your Bonus Action for that turn.

PHB P78, emphasis mine:

Flurry of Blows. 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 Martial Arts:

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 in your turn you choose one or the other as indicated here PHB p 189 under Bonus Actions:

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.

You will have to choose one feature or the other as they both consume your only bonus action. You will have either 3 attacks with the Martial Arts feature or 4 with Flurry of Blows.

PHB P78, emphasis mine:

Flurry of Blows. 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 Martial Arts:

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 in your turn you choose one or the other as indicated here PHB p 189 under Bonus Actions:

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.