Heat oil in wok or large skillet until very hot. Cook and stir garlic and ginger in the hot oil until fragrant, about 30 seconds. Add the water chestnuts, snow peas, mushrooms, red pepper flakes, salt, pepper, and shrimp to the pan. Cook, stirring, until shrimp turns pink, 2 to 3 minutes.

Combine the chicken broth, rice vinegar, fish sauce, and dry sherry in a small bowl. Pour into the shrimp mixture; cook and stir briefly to combine. Combine the cornstarch and water and stir into the wok. Stir until sauce has thickened, about 2 minutes.