In a medium saucepan bring 11⁄4 cups water to boiling; stir in freekeh.
Return to boiling; reduce heat. Cover and simmer for about 20 minutes or until freekeh is tender and most of the water is absorbed.
Place freekeh in a fine-mesh sieve; run under cold water. Drain well. (If using bulgur wheat, just cover with boiling water and soak for about 20-30 minutes, until soft.)
Meanwhile, using a paring knife, cut off a thin slice from both ends of each grapefruit. Working with one grapefruit at a time, place a flat end on a cutting board and cut away the peel and the white part of the rind, working from top to bottom. Working over a large bowl to catch the juices, hold the grapefruit on its side and cut into the center between one section and membrane. Cut along the other side of the section next to the membrane to free the section. Repeat with remaining sections. Place sections in a bowl with juice. Squeeze membranes over the bowl to extract as much juice as possible before discarding.
Add freekeh (or bulgur), chickpeas, avocado, cucumber, scallions, parsley, and mint to a bowl with grapefruit. Toss gently to combine.
Season with salt and pepper.