Wordy Bird flew quickly.
Quicker is not an adverb. It should not modify a verb. Quicker is an adjective, hence the following is wrong:
It should be:
Nestmate (thought he) flew more quickly than Wordy.
Quicker can be used like this:
But Wordy knew she was quicker.
Quick is the positive adjective. Quicker is the comparative degree of quick. Quickest is the superlative degree of quick. They are all adjectives. And adjectives modify nouns, not verbs.
Put it together and what have you got?
Nestmate was not very quick. He could not fly quickly at all, and his strides were about as quick as a worm in dried mud. In fact, among the quicker members of the nest, he had quickly earned the affectionate yet dubious nickname Slow-walkin'-Jones-slow-talkin'-Jones. It was a nickname none could say quickly. (In truth, Chickling was the quickest of the three.)
But of course there are always exceptions to the rule. Quicker and quick are sometimes used as adverbs in idiomatic speech. So in dialogue, Chickling might say:
"Mummy, come quick!"
To which Wordy Bird would, of course, reply:
"I'm coming as quickly as I can."