Soak the cedar plank in water for at least 1 hour.
In a small, nonreactive saucepan over medium-low heat, combine the soy sauce, vinegar, and sugar. Cook until reduced by half, about 20 minutes. Remove from the heat and add the garlic, ginger, and red pepper flakes. Cool slightly and then whisk in the oil. Reserve ½ cup of the glaze for basting the chicken.
Put the thighs in a large bowl, pour in the glaze, and toss to coat. Refrigerate until you are ready to grill.
Prepare the grill for direct and indirect cooking over medium heat (350° to 450°F).
Place the soaked plank over direct medium heat and close the lid. After 5 to 10 minutes, when the plank begins to smoke and char, turn the plank over.
Remove the thighs from the bowl and discard the glaze. Arrange the thighs on the smoking plank and cook over direct medium heat, with the lid closed, for 5 to 10 minutes. Then move the plank over indirect medium heat and continue cooking, with the lid closed as much as possible, until the juices run clear, 20 to 30 minutes, basting occasionally with the reserved glaze during the last 10 to 15 minutes of grilling time. Remove from the grill and baste with the glaze once more before serving.