Bullet Bill Base is a tall tower. There are moving clouds here as well as many Bill Blasters. Grab a Super Bell and go to the wall that's moving up. Climb up it and the nearby clouds to reach the first Green Star at the very top. Go below the level with the crates for the warp box to the midpoint. Climb the back wall for a Mystery Box. Climb the wheel to reach the second Green Star. When you return to the main level, you'll find moving Bill Blasters to dodge. In front of the wall to the right, is an invisible block with a 1-up high above. Ahead are moving clouds and walls, as well as a Banzai Bill. Take the moving walls up and to the right for the third Green Star. Up and to the left, you'll find the stamp over some brick blocks. Go to the right and you'll find the flag.
The stamp is of a defeated Goomba.