For this method you'll need a second controller.
I found it easiest to set up a local game with the arena set to Classic and the mode to Capture The Flag. Set the round timer to 2 minutes and the matches per game to 9.
In this game mode both players start on opposite sides of the arena with a small pathway between them. So you never need to really worry about blowing up blocks to reach the pick up.
I found it best to head over and pick up the enemy flag then wait for the clothing pick up to appear (it'll appear when there's about 1 minute left on the timer), grab the pick up and then finish the match by returning to your base with the flag.