Make marinade: Mix all ingredients together and pour over meat in a shallow dish. Chill at least 1 hour and up to 3 hours ahead.
Make salsa: Combine all ingredients in a medium bowl. Let sit, stirring occasionally while you cook meat.
Prepare a grill for high heat (450° to 550°; you can hold your hand 5 in. above cooking grate only 2 to 4 seconds). Cook meat 8 to 10 minutes. Let rest on a cutting board, covered with foil, for 15 minutes. Chop meat into 1/2-in. pieces.
Assemble burritos: Lay 1 tortilla on a work surface. In the center, arrange 3/4 cup beans, 1/2 cup salsa, and 1/2 cup meat. Roll burrito up, folding sides in over filling. Repeat with remaining ingredients. Serve burritos with remaining salsa.
*Buy flap meat (also called flap steak or bavette), a thin, flat piece of beef from the flank area, at Latino markets.
Note: Nutritional analysis is per serving.