To get more specific with the data, you'll have to make a tradeoff on another item. Beyond realizing that certain zip codes are not going to have many people of certain races/ethnicities and that some zips are just low populated overall, you're going to start to see suspect information (outliers both high and low) for a small geography like zip codes.
Additionally, the race-based tables have their own structure, as can be seen in B01001B for Black, B01001D for Asian, etc. The age categories are 10-14 and 15-17, so trying to get this for 12-15 year olds starts to stretch the assumption that such ages are evenly distributed throughout the age category. So the data exists but it will both be a fair amount of work to download for each race as well as having some reliability issues for this specific narrow age range at the zip code level. A potential tradeoff would be to compile the race data for all children under 18, but even then in remote low-populated (rural) areas the data will be prone to error. ACS data from the sample would have to be used with caution. 2020 Census data on this should be out late this year or next spring, but no one is for sure how its accuracy will be impacted by the implementation of Differential Privacy controls. Best wishes!