If I'm a monk that is being grappled by a monster, can my Way of the Open Hand Flurry of Blows effect to push a creature 15ft away from me break that monster's grapple on me?
You can do it! The Grappled condition does not prevent you from attacking, it only restricts your speed, and can be broken by pushing someone away (third point):
A grappled creature’s speed becomes 0, and it can't benefit from any bonus to its speed.
The condition ends if the grappler is incapacitated (see the condition).
The condition also ends if an effect removes the grappled creature from the reach of the grappler or grappling effect, such as when a creature is hurled away by the thunderwave spell.
Since you can use Attack, you can use the Open Hand Technique, the second effect of which will satisfy one of the conditions to end the grapple:
Open Hand Technique
Whenever you hit a creature with one of the attacks granted by your Flurry of Blows, you can impose one of the following effects on that target:
(skipping the other effects...)
- It must make a Strength saving throw. If it fails, you can push it up to 15 feet away from you.