i generally don't even bother trying to make up for the flavor, i just deal with it being a little diluted. but i also don't really use much flavoring, about 2 drop per mL depending on the flavor some seem to be more potent than others... plus i use 24mg so its already pretty strong. but how much flavor do you mean when you say a lot?
because it think 10% would be a lot and that would only drop you 12mg/mL to 10.8mg/mL so just a little more than 1mg i feel like is fine. but if you really want it to be 12mg (or really really close) get a stronger strength like zoi said and dilute to like 13.32mgs (111% of 12) and then add your 10% of flavor (13.32 x .9 [or 90%] = 11.988mgs)
its always fun to make sure you remember your basic algebra to

if you want something stronger just add on the percentage to 100 and go from there until you get something that is basically the mgs you want. if you want 15% i just multiply the mgs you want by your flavor percent added to 100 (you will see you need to add a little more than that), and then multiply the total by the flavor percent subtracted from 100: 12 x 1.15=13.8; 13.8 x .85=11.73.... 12 x 1.16=13.92; 13.92 x .85=11.832.... 12 x 1.17=14.04, 14.04 x 11.93...)