Tiger claw says that you can ADD half str to one of the rolls so take 3 away and i think you are about rigth. That is assuming your GM let you stack extra damage from dragon and Tiger. But this is not really special i think. If you go monk 2 bloodrager 3 (to avoid aligntment stuff) you can get about the same on a flurry with dragon alone. Spend one of the feats you save on weapon focus and you will be about where your guy is. Also dont spend your human feat on IUS. Just use a great sword until level 3, where you take first level moms. And take fuirous focus as human if you want to do the Tiger/Dragon combo.
A level 5 figther can get+11 to hit, (weapon dam)+15(+6(str 18) +6 (pa) +2(spec)+1 (weapon training)) with a better weapon and after a move, with out needing 2 swift actions to get the trick ready. Not as high but overall more usefull i think.
My point is that it May be a fun guy to play but he will not break the game and the only nigthmare is if the GM wont ignore the no raging for lawfull guys.
If you get moms at 3 and 5 you can skip IUS.also getting moms al the way to 4 will give you still mind for monastic legacy and ki for that little extra. And will only cost you 4 rage rounds a Day and a load of hit points.
Yes main problem is gonna be the two swift actions. And at higher levels pummeling style and flurry is gonna be better.
This would be a little awkward of a build, to be honest. I think any GM paying attention is going to wonder, what with Barbarian and Monk not normally multiclassing with each other well. 'A barbarian who becomes lawful loses the ability to rage .... ', and your alignment's going to determine which class CAN advance. Master of Many Styles still has to abide by the alignment requirements.
The only way this combination can really work is with an Assimar with the sub-race and trait that permits him to be a Monk of neutral good or true neutral alignment.
Or as mentioned further up Bloodrager.
The example given is a Barbarian though -- but replacing that class with Bloodrager would be the simplest "fix".
Aligment is not a problem. Start with monk, then become non-lawful, you lose nothing.
The original poster didn't; the first monk levels were taken at 4th, which is why Improved Unarmed was a first-level feat. Not sure if this build would work with the monk levels taken first. And remember, once you're unlawful, no more adding monk levels.
Edit: As written, with monk levels at 4 and 5, forcing lawful alignment at THAT point..that 22 Strength goes down to 18, as there's no raging while lawful. -2 to the base damage bonus, yay!