Over the years I have used both methods. Finally coming to the conclusion that I prefer to NOT flour prior to browning. My goal in browning stew meat is to brown the meat itself extracting as much blood and goo out of the meat as possible. I do this over a high BTU outdoor burner. If this "stuff" is not removed at this point it will show up in the pot as scum.
Which can be skimmed off if you see it. I also run the meat through a collander to wash off excess fats/oils etc. So I go to the pot with browned meat with as little fat and fat soaked flour as possible. Admittedly, Some fat and browned flour are added back later in the process in the form of roux to make the gravy. Using this method I have total control over the contents, color, and flavor of the thickening agent.
Don't laugh at me!! I'll come get ya!!