Heat a non-stick frying pan over medium-high heat. Add kimchi. Saute until fragrant and slightly yellow, about 5 minutes. Add sesame oil; cook until kimchi is coated, 2 to 3 minutes. Pour in vinegar to coat the bottom of the pan. Increase heat slightly; bring vinegar to a boil. Add sugar. Reduce heat to low; cook until sugar dissolves and kimchi is browned, about 3 minutes.
Do not drown the kimchi in vinegar! Just use enough so that it coats the pan. Kimchi is already prepared with vinegar so you do not want to use too much.