First, let me say that you are right, "quickly" is an adverb.
Second, let me state that I will not tackle whether you should avoid adverbs and adjectives.
Third, let me say that there is a way to read "quickly" and have it be an adjective.
Consider this example:
"After a quickly meal of rations, I was pumped up and ready to go." (
here)
Most likely this is just a slip for "a quick meal". If you look at the context, the guy didn't have much sleep and needed to replenish his energies. It's not a stretch to think he didn't have much time to eat: thus a quick meal.
But...
...there is a different way of reading the "quickly" - resulting in a different meaning. Let me make a grammar detour:
"Quickly", as I said, is an adverb. Breaking it down, it consists of the adjective "quick", and the "derivative suffix" "-ly". "Derivative suffix" is a technical term that means that you can use the suffix to derive a new word class (here "adverb") from another wordclass ("adjective").
But "-ly" doesn't only derive adverbs from adjectives. It aslo derives adjectives from nouns. Thus:
man
+ -ly = manly (adj)
coward
+ -ly = cowardly (adj)
Usually, these structures have the meaning of "like a [noun]" thus "manly" means "like a man", and "cowardly" means "like a coward". But occasionally, you get adjectives that have been formed like that but have developed a meaning of their own:
Take the adjective "kindly", as in "a kindly person", which has a meaning very similar to a "kind person". This is quite a bit more complex and involves a cultural metaphor of "kin".
You still have:
kind (n.) + "-ly" = kindly (adj.)
This is a special case in which a regular adjective (kind) exists side by side with a derivational adjective (kindly), and where the derivational adjective looks exactly like the adverb of the regular adjective. This can be quite confusing, but it actually makes sense once you work it out.
"Quickly" could be like that. But the difference is that the meanings between the adjective "quick" and the adjective "quickly" would be farther apart than "kind" and "kindly".
So what we're looking for is a noun "quick". What we do have is "the quick" as in "cut to the quick". The quick is the sensitive skin under your finger and toenails. As a metaphor, "the quick" is often the essence.
What then could a "quickly meal" be? I can imagine reading this as a rather unusual way of saying "an invigorating meal".
Yep, it's a stretch. Ignore me. "Quickly" is an adverb.