I believe his parents are Jacob Brill and Margaret Zoeller.
I had tentatively had that info, based on knowing his mother's maiden name was "Joeller" and that he was born in Louisville, KY. After some digging, I found the above mentioned couple with a son named Walter, who lived in Louisville, with dates that were similar. The record you posted above that states Walter's "next of kin" was Mrs. Jacob Brill seems to confirm that.
Jacob and Margaret appeared to have immigrated from Bavaria, Germany. But I don't have much more on them than that (and their other children's names) at this time.