
Mathmuse |

If an archetype says that the monk loses uarmed strike, then the monk loses the entire ability named "Unarmed Strike." That includes the Improved Unarmed Strike feat, having unarmed strike count as a manufactured weapon and a natural weapon, and the damage progression.
Brawler levels counting as monk levels would make no difference, because even monk levels would not have a damage progression. However, the brawler/monk would still have unarmed strike damage increase with brawler level due to the Brawler's Unarmed Strike ability.
If the archetype says that the monk loses Improved Unarmed Strike, that is not the name of the ability, so he would lose only the feat. He would get the extra damage, etc., but would provoke while making unarmed strikes.

Mathmuse |

The Brawler Martial Training ability also has the clarification statement, "This ability does not automatically grant feats normally granted to fighters and monks based on class level, namely Stunning Fist." Nor does it grant abilities normally granted to fighters and monks based on class level. The writers did not add that to the clarification because they thought it was obvious.
When a monk archetype trades away a monk ability, then that ability is no longer part of monk levels.
For further discussion, you should post the relevant lines from the archetype so that we can see whether it has any loopholes that we can exploit.

Claxon |

I'm not sure I understand the exact question, but:
As I understand it Monastic Legacy will do nothing for you. Brawler levels count as monk levels (IMO) for it, and the monk levels despite having lost unarmed strike damage improvement still are monk levels. So you have no non-"Monk" levels.
MOnk's Robe should work just fine, and increase your unarmed strike damage by 5 brawler levels.

Mathmuse |

Ah, Claxon found the loophole that Nekomimi^w^ wanted. I had not checked the exact wording of Monk's Robe, because 8 years ago I played a monk with such a robe and thought I remembered its details. But I had forgotten what the robe did for a non-monk.
Monk's Robe
Price 13,000 gp; Aura moderate transmutation; CL 10th; Weight 1 lb.When worn, this simple brown robe confers great ability in unarmed combat. If the wearer has levels in monk, her AC and unarmed damage are treated as a monk of 5 levels higher. If donned by a character with the Stunning Fist feat, the robe lets her make one additional stunning attack per day. If the character is not a monk, she gains the AC and unarmed damage of a 5th-level monk (although she does not add her Wisdom bonus to her AC). This AC bonus functions just like the monk's AC bonus.
The monk's robe gives a non-monk the AC bonus and unarmed damage of a 5th-level monk. Though Nekomimi^w^'s monk/brawler is a monk, it is still reasonable that it restores the missing unarmed damage to an archetyped monk that traded the ability away--the writers of the wondrous item simply failed to imagine a monk without those core monk abilities and did not adapt the phrasing.
Thus, the archetyped monk with a Monk's Robe would gain the unarmed damage of a 5th-level monk. Since the brawler's Martial Training is supposed to make brawler levels stack with monk levels for unarmed damage, the brawler's level will further progress the unarmed damage gained from the Monk's Robe. However, the levels of archetyped monk won't help progress the unarmed damage from the Monk's Robe, because the abilities of the archetyped monk essentially say, "Hey, my levels don't get unarmed damage progression. More levels of no progression is still no progression."