Heya @Vicjoaid
Unfortunately kerridoc isn’t on the forums anymore.
To answer your question, with costumes the only boosted Special Skill % comes from feeding a duplicate COSTUME PATTERN. so if you summon multiple copies of hawkmoon costume from the costume chamber, you can feed the duplicates for a 50% chance as Special Skill going up.
As with base hero leveling up, when the costume level is maxed but the special skill is not, further feeding grants a 5x multiplier on the. Chance of special skill increase (as noted with a red 3*. Normally = 6%, boosted = 30%)
There are some graphics and more information in the costume FAQs thread. Specifically in Q2 and Q6 hidden pictures (where it says click for pictures)