Sorry, I do not know of an Arthur Kloetzke.
I know only my grandfather's name, Otto Rudolph Ferdinand Kloetzke, and his father Albert Ludwig August Kloetzke, and his mother's name Catherine Brandt.
There was a bother, or maybe more than one brother, who lived in USA prior to 1910.
Otto spoke of the name Kloetzke having been shortened and "Germanised" from a longer name that was not of German origin in an earlier generation, that is, prior to his birth in 1889. This name is so uncommon that it seems likely all of this name are connected if only we could trace it!
I have found record of Albert Ludqig August Kloetzke in Berlin, his mother's maiden name being Brezchetznick.
I don't suppose this is any help, but it is all I know of the family.