Birds have been on flags, coats of arms and on shields since at least the early middle ages, especially eagles. The US still has a thing for eagles these days.
Wings can be a sign of your freedom, your range, your power, you name it. Birds are just neat.
The bird on the Gravesfield coat of arms seems to be a swallow, just like the bottom set of wings on the imperial logo (based on the wing shape). I don't know what kind of bird the bigger set of wings is supposed to be, probably an eagle because nobility isn't very imaginative. You can see the big set of wings at the bottom of the Gravesfield coat of arms, but on the emperor's symbol those wings have been placed on top and moved into focus.
I think the wings represent Belos and his brother. Belos was not as powerful in the human world as his brother so his wings are dangling of the human symbol, but in the magic realm he's the Big Guy.
IMO the real interesting parts of Belos' logo is the sword and shield. In a world where you can throw ice and summon sludge golems, the sword and shield are useless relics of the human world. However, in the 1600s humans were already killing each other en masse with canons and guns, which would probably be incredibly effective against witches.
Also the Gravesfield coat of arms is upside down. Maybe that also means something. Maybe the artist just thought it looks neater this way.