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If I am correct, then ぶっかける and やがる are verbs but what is the き doing in between them?
Full sentence: ~ この辺では、言葉に気をつけた方がいいぜ。町のこちら側に住んでいるやつらは、口笛を吹いただけでも顔に唾をぶっかけてきやがるからな。 ~ You have to be careful about what you say around here. People on this side of town will spit in your face just for whistling.
There are three components:
The difference between ぶっかけやがる and ぶっかけてきやがる is that the latter has くる（来る） → き in it. If you remove やがる and make it more polite, the expression would be ぶっかけてくる.
By having くる in it you make it clearer that you are the presumed recipient of the action. In this case, the interpretation that there are third-party recipients are unlikely so it doesn't add much, though.
Notice that whose 顔 is unspecified in Japanese, unlike "your face" in your translation. I think くる provides the same information in a different way.
