Flame angels are immensely sensitive to ammonia (new tank syndrome) and lower oxygen conditions. Do you have a powerhead or sump/skimmer? How long has your tank been set up?
Some strains of velvet also impact angels in particular by killing them via gill damage before you see spots on the fish. Lethargic behavior, hiding from light, loss of color, sudden loss of appetite are however often witnessed in these casss. They may also swim in to what flow you do have.
Flames are very unforgiving with regard to ammonia and lower oxygen conditions they’re not an ideal fish for a tank newer than 6 months old.