The Death Eaters are a group wizards and witches who are led by Lord Voldemort. Since this is the case they can fly if using a broom.
However, if you mean Dementors (the dark beings who sucks the soul of of their victims) then yes, they can also fly in the movies. This is shown in the first five minutes of the Harry Potter and the Order of the Phoenix movie where they fly against Dudley and Harry when these two are inside a tunnel.
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To see who comprises the Death Eaters, check the Harry Potter Lexicon. (http://www.hp-lexicon.org/wizards/death_eaters.html) The Death Eaters.
Answer: Yes, as they are not pure-blood witches or wizards and not what Death Eaters like. Death Eaters don't like anyone who isn't pureblood and not a blood traitor. Answer: Not known.
They’re only the Death Eaters’ “natural allies” because the Death Eaters provide them with more victims when they’re in power. However, Death Eaters are not immune to Dementors, and Dementors don’t care much about the moral alignment of their dinner.
Harry kills Voldemort Voldemort Kills Snape Voldemort kill Robert pattison Snape kills Dumbledore someone kill Barty Crouch Deth eaters kill Fred weasley Deth Eaters kill tonks deth Eaters kill lupin Death eaters kill moody ...the death eaters kill a few,don't they?
They probably thought his job wasn't good enough for a pureblood or something. Plus, the children hate Filch and the Death Eaters would have liked that. Plus, we don't know if they hated squibs or not.