The adjective nice can be inflected: nicer, nicest. Can the derived adverb nicely be inflected as well, or does it only have the absolute form?
According to the wikitionary, "more nicely" is the comparative form.
There is a grammar rule in English that adverbs in -ly and participles have forms of comparison with "more" and "most". There are some adverbs with forms of comparison in -er/-est as early, earlier, earliest. The Longman English Grammar by L. G. Alexander has "The comparison of adverbs" in paragraph 7.4.