I have two personal theories;
Fletcher is a Slytherin (because he is involved in many illegal activities).
Fletcher is a Hufflepuff (because he was deeply loyal to Albus Dumbledore).
I don't think he is a Ravenclaw (because he is somewhat a dimwit), neither a Gryffindor (because he is a coward).
What house at Hogwarts was Mundungus Fletcher in?