It's not a question, it's an embedded wh- clause, so you don't need an auxiliary
By the way, I think it's better to put "in modern society" at the front of the sentence. Otherwise "kiss in modern society" looks like a single phrase (it's not: you mean "kiss + in modern society")...not sure if you see what I mean?
In any case here's what I would write:
"In modern society, relationships are affected by how we kiss"