You are right, your DM is wrong.
The description of Flurry of Blows 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.
That’s it. Nothing about spending more ki points for more attacks. You may spend 1 ki point for two unarmed strikes as a bonus action; you may only take one bonus action per turn.
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. (Ch-9, Basic Rules, p. 72)
As a counterexample, the Way of the Four Elements monk has an ability that allows for spending additional ki points to enhance the effect:
Fists of Unbroken Air.You can create a blast of compressed air that strikes like a mighty fist. As an action, you can spend 2 ki points and choose a creature within 30 feet of you. That creature must make a Strength saving throw. On a failed save, the creature takes 3d10 bludgeoning damage, plus an extra 1d10 bludgeoning damage for each additional ki point you spend, and you can push the creature up to 20 feet away from you and knock it prone.
If Flurry of Blows were intended to allow for additional ki expenditure for more attacks, we would see similar wording there.