Trim fronds and stalks from fennel bulbs, setting aside several small fronds for garnish. Cut bulbs in half lengthwise, cut out core, and slice very thinly lengthwise on a handheld slicer. Slice shallot very thinly on slicer (you should have about 1/4 cup), and put both in a large salad bowl.
Trim peel from oranges. Working over bowl to catch juices, cut oranges into thirds straight down through top of fruit; then cut crosswise into thick pieces and let fall into bowl.
Cut lemon in half crosswise. Set a strainer over same bowl to catch seeds and, twisting a fork into each lemon half, juice them into bowl.
Add oil, salt, and chile flakes to bowl and toss salad gently but thoroughly. Taste and add more salt and chile if you like. Toss again and top with fennel fronds.