It probably doesn't need to be in a dictionary because it's just a compound of two words, rarely used as a singular word until recently, except in the specialist field of distilleries. It could just as easily be written as "wash back" or "back wash" or "backwash" or "back flush" or "backflush" (backflush is usually used in a different context, but technically has the same literal meaning). You can use these terms in any context you wish - it might not be common but because they're just combinations of 2 simple words, it should still be understood.

"Washback" is a education-related instance of what is generally called "perverse incentive." A well known internet encyclopedia has English-language articles on washback and perverse incentive. A similar word, "backwash," is a moderately common term for a negative reaction or result. I've encountered the word from time to time in news articles, probably as an attempt to replace the common word backlash.