No, it doesn't stack.
The ability lacks a text saying it should stack with your monk levels, or another class that grants monk levels. Like it does for your AC Bonus class ability:
This counts as the monk ability of the same name, and the sacred fist’s warpriest levels stack with monk levels for determining the benefits.
As an example of this, we got the Brute Vigilante, the both Brother of the Seal and Champion of Irori prestige classes.
Heavy Punches (Ex): The brute eschews civilized combat and prefers to wade into a fight with his fists swinging. While in his vigilante identity, the brute’s unarmed strikes deal damage as if he were a monk of his size and vigilante level. If he has levels in other classes that provide monk advancement for unarmed strike damage, his vigilante level stacks with those levels whenever he is in his vigilante identity.
Unarmed Combat (Ex): A Brother of the Seal’s class levels stack with any monk levels for the purposes of determining his flurry of blows, stunning fist, and unarmed strike class features (including determining damage dealt by his unarmed strike attacks).
Martial Artist (Ex): The class levels of a champion of Irori stack with monk levels for determining the effect of his AC bonus, flurry of blows, stunning fist, and unarmed strike class features.