With a sharp knife, cut off and discard peel and outer membrane from 2 mandarin oranges or tangerines (about 1/2 lb. total). Hold fruit over a bowl and cut between fruit and inner membranes to release segments into bowl; squeeze juice from membranes into bowl, then discard membranes. In a 1- to 1 1/2-quart pan over high heat, stir 1 tablespoon minced garlic and 1 tablespoon minced fresh jalapeo chili in 1/2 teaspoon salad oil until garlic and chili begin to sizzle, about 1 minute.
Add 1/2 cup mango chutney, 2 tablespoons rice vinegar, 1/8 teaspoon hot chili flakes, and mandarin segments and their juice. Stir until boiling, then reduce heat and simmer, stirring often, until mixture is reduced to 1/2 cup, 8 to 10 minutes.
