"Slower" is a comparative adjective, while "slowly" is an adverb. According to the formal rules of grammar, the comparative form of "slowly" is "more slowly." That said, I would only use "more slowly" in formal writing. In real life, people use "slower" as if it were an adverb.

I would say the proper way to form that sentence is by using the word “slowly” because you’re describing how the person is speaking, it’s an adverb (adjective + verb) “speaking (verb - how?) slow(ly <-adverb). And the word “slower” slow (er - in comparison to something) would be used if you had another person to compare them to, for example: “The teacher spoke slower than my classmate so that I could understand”! Hope that isn’t too confusing, the best tip I can give you is to differentiate the words is by asking yourself questions such as “how?” and “in comparison to who?”

slow -- slower -- the slowest but slowly -- slowlier -- the slowliest