O.Henry did it again! The hero is telling about a dream of going to heaven, and awaiting judgment.
"A fly cop--an angel policeman...."

Another trope! Dissent if you must.

A fly cop should not be confused with a French flic or Weird Al Yankovic's Fly Rabbi. Fly, adjective, 'keen, artful; fanshionable, stylish' from about 1811.

from about 1811
and Offspring thought they were being so hip:

"pretty fly for a white guy"
http://thesonglyrics.com/o_song_lyrics/theoffspring_lyric1.html

It's hip to be hep, Daddy-O. Nothing new under a Blue Moon. Offspring, that was the non-parody version band name. Thanks.