Two! You can either use your claw attacks (d4) or you can use your flurry of blows class feature to make two unarmed strikes (d6), but take a -2 on both attacks.
As for your build, Irori is probably your friend. If you want to be a good punchy guy, Cleric of Irori with the Crusader archetype and the Strength(Fist) domain is a good start. If you want some really neat tricks go Divine Paragon archetype and you'll end up with the Deific Boons of Irori.
Unchained Monk "only" gets two bonus attack from Flurry (one at 1st level, the second ad 11th level). In addition, bonus attack come from spendign a Ki point, and from Haste, Blessing of Fervor, or a similar effect. Under normal circumstances, that results in up to 8 attacks per round, three of which are at reduces attack bonus, so if you want to roll all your attack rolls at once, you'd need distinguishable dice for each one of those.
I don't really understand the basics of your character, could you go a bit more into that? DO you plan on multiclassing, or do you gain the benefits of both classes at the same time (called gestalt)? And what racial bonuses does your character get?
@Turambar: Unchained Monk's Flurry doesn't have the -2. In addition, it should be noted that Flurry can be used with a multitude of weapons, some of which deal up to 1d10 damage.