You knew that red Skull Gem of Flavio’s was going to come in handy at some point in Paper Mario: The Thousand-Year Door, and here it is. During Chapter 5, you find a skull-shaped door and it seems like the skull-shaped gem might have something to do with unlocking it. Convince Flavio to hand it over, and you’ll meet with the ‘Stache Brothers Red and Blue.
To reiterate, this all happens in Chapter 5. About halfway through the chapter, you’ll find the skull door. Eventually, you’ll return to Flavio who will follow you back across the island to see it for himself. You can then convince him to borrow the skull. It slots into the door, and the ‘Stache Brothers Red and Blue rise from the ground.
The hint for completing this is in Flavio’s song, which he will helpfully start singing soon after the ‘Stache Brothers’ appearance.
The song first mentions Red ‘Stache “landing on his end” three times. What this means is that you need to jump on top of the pillar with the red mustache and do a spin jump (ground pound) three times.
You’ll then need to move to Blue ‘Stache. The song says he’s whacked four times on the belly. That simply tells you to hit it in the face three times with your hammer.
The skull door will then (partially) open. Grab Admiral Bobbery and toss him up on the ledge that opened. He’ll walk in and detonate, blowing the door open.
Flavio will mourn the loss of his treasured Skull Gem, but it is quickly returned to him.