From the Super Mario Wiki
The Flab Boys are two large, overweight rappers from the city of Rap Land. They look very similar, and there is a possibility that they may be brothers, but their relationship was never mentioned. The Flab Boys take their name from the real-world rappers, The Fat Boys.
In The Super Mario Bros. Super Show! episode "Bad Rap", Rappin' Koopa had taken over Rap Land by invading the castle, tying up King James, and playing a hypnotic theme through the speakers all over the city. The Flab Boys were unaffected, due to the fact that they were wearing earphones.
The Flab Boys soon meet up with Mario, Luigi, Princess Toadstool and Toad when they arrive in Rap Land, and give them the lowdown on what's happened. The Flab Boys then accompany them to the castle, where Princess Toadstool tries to sneak Toad in. When Princess Toadstool's cover is blown, the Flab Boys try to stop several Koopa Troopas by hurling records at them, but they fail. Mario attacks the Koopa Troopas with his plunger, but Princess Toadstool simply winds up in the arms of Rappin' Koopa.
Fortunately, Toad managed to rescue both Princess Toadstool and King James, and they met up with the Flab Boys and the Mario Bros. outside the castle. King James then decided that unplugging the Royal Plug was the only way to stop Rappin' Koopa's music. The Flab Boys and Luigi gave Mario a boost, allowing him to reach and unplug the cord, shutting off Rap Land's power.
The Flab Boys later assisted Mario and the others in a rapping duel and managed to defeat all of Rappin' Koopa's Koopa Troopas by rolling down a hill and knocking into them. After Toad managed to trip Rappin' Koopa, the Flab Boys threatened to sit on him. Unfortuantely, Rappin' Koopa managed to get away through a Warp Zone.
After returning the castle, the Flab Boys offered to play the Mario Rap, which everyone danced to, as a celebration of Rappin' Koopa's defeat.