If you are speaking in metaphors, you are said to be speaking metaphorically. But if you are speaking in similes, how are you said to be speaking? Similarly?
I don’t think there’s a specific adverb. Figuratively covers it as a more generic term. I think you’re stuck with in similes if that’s the specific meaning that you want to convey.
ETA: I don’t think you can use comparatively. Although in principle it seems like the word might be able to mean “using comparisons”, in practice it’s not used that way, and people might just think you left a word off the end of your sentence:
He was speaking comparatively… quickly?