My aasimar brawler can make three attacks per round using Greater Two-weapon Fighting. I'm debating taking the feat Metallic Wings—I already meet the prerequisites—which grants 2 wing attacks that are secondary natural attacks. Can I make, in the same round, three normal attacks and the two wing attacks?
Brawler's Flurry: No natural weapons.
The Brawler hybrid class is quite clear on this issue. A Brawler does not get Greater Two-Weapon Fighting as a bonus feat - instead, they can make a flurry as a full-round attack as though they had that feat. Furthermore, the flurry is a full-round action consisting of unarmed strikes, close weapons, or monk weapons, but not natural attacks. As a special full-round action, you can't make further attacks after it's done that round*. From the class description:
A brawler with natural weapons can't use such weapons as part of brawler's flurry, nor can she make natural weapon attacks in addition to her brawler's flurry attacks.
Through the Brawler's Flurry, the attacks you can make are based on your Base Attack Bonus (which enables more iterative attacks in a full attack) and your Brawler level (which temporarily lets you use Two-Weapon Fighting, Improved TWF, and Greater TWF in your flurry).
*=I believe the monk's flurry of blows also follows this rule, but this seems to be debatable.
Full-attack without Brawler's Flurry: Yes natural weapons.
Alternatively, you have the option to make a full attack with all of your normal weapons (including unarmed strikes) and your natural weapons together. This is separate from the Brawler's Flurry. On one hand, more attacks means more chances to hit. On the other hand, some of these attacks are weaker and less reliable.
This is how a full attack works when you combine the two:
- First make all of your iterative attacks using your unarmed strikes.
- If you actually have Two-Weapon Fighting, Improved TWF, or Greater TWF (as selected feats, not temporarily through Brawler's Flurry) then you may include those extra attacks. Remember to apply the proper penalties to the attack rolls.
- Unlike in a Brawler's Flurry, attacks made with your offhand will only use half your Strength bonus to damage.
- Once you make all of your unarmed attacks, you can attack with your natural weapons, but all of them count as secondary natural weapons (use BAB - 5 instead of BAB for the attack roll, and apply half your Strength bonus to damage). In your case, this isn't a problem because Metallic Wings are secondary attacks anyway.
So for you, the answer is technically yes, but only as a full attack and not in a Brawler's Flurry.