Toast the glutinous rice in a dry skillet over medium heat, stirring constantly, until deep golden and nutty, 8–12 minutes; cool, then grind to a coarse powder.
In a bowl, whisk together the fish sauce, lime juice, granulated sugar, and Thai chili flakes until the sugar dissolves; set the dressing aside.
Add the water to a large skillet over medium heat and bring to a gentle simmer. Add the finely chopped chicken thighs and cook, stirring and breaking up clumps, until just opaque with no pink remaining, 4–6 minutes.
Remove the skillet from the heat. Sprinkle in all the ground toasted glutinous rice and pour in the dressing; toss until the chicken is evenly coated and slightly thickened by the rice powder, 1–2 minutes.
Fold in the shallot (thinly sliced), green onion (thinly sliced), cilantro (coarsely chopped), and mint leaves (lightly torn) until just combined.
Transfer the larb to a serving dish and serve warm with cabbage wedges, cucumber slices, and lettuce leaves.