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.
