Ain't = Haven't = Have not
"Ain't never had" = "Have not never had" which is a double negative, which by formal literal definition reverses the meaning into a positive ("have had"), but in popular slang only reiterates the negative (like "have never ever had").
Also, in this sentence, "any" may be a lazy way of saying "anyone", but it's hard to know without seeing the context in which this statement was used.
Therefore: "I ain't never had any make me feel this way" = "I have never had any(one) make me feel this way".