From this picture (Chapter 13 Illustration, The Vile Village. Picture Edited), we can almost prove that V.F.D stands for Volunteer Fire Department. Because, of Quigley in The Slippery Slope, we know the 'V' stands for 'Volunteer'. The torn notebook page at the bottom has a large letter "F" and the lowercase letters "ire". In the top left hand corner, there is another piece of torn paper. On it is written a large "D". Folloing it id either "epot" or "epa". The only noun that that begins wqith "Depa" is Department. So we have either "Volunteer Fire Department" or "Volunteer Fire Depot"