Answer:
The irony is in saying that seeing a dog wearing pants (parody of breeches) was an uplifting or edifying sight which is really not true and which is comical when visualized.
Explanation:
An irony is expressing ones thoughts in words that mean the opposite to achieve humor. The narrator in this instance was looking down on the fireman by comparing him to a dog wearing pants and a feather hat.
He thus compared him to an animal and in the same instance, said that it was an edifying sight. He also called him a fine chap in the same breath. This is quite contradictory and that is how he achieved the use of irony in those lines.
An adverb is much like an adjective it's actually the words adjective adverb smooshed together so think of it as a word that is describing the verb