I cannot fly with the wings and putting them into the cape slot does nothing to fix this.
Heres my mod list:
All my mods should be fabric expect one
YUNGS Better caves
Better-end
Better-nether
byg
cloth-api
fabric-api
geckolib-fabric
guardians-galore
icarus-1.2
Origins-1.16.5-0.7.3
Origins-Classes-1.16.5-1.1.1
Requiem-1.7.7
RoughlyEnoughItems-5.11.218
TooManyOrigins-1.1.6.5-0.13
Trinkets-2.6.7
Xaeros_Minimap_21.8.2 (Forge)
YungsApi-1.16.5-Fabric-5

As for my output log/file log:
Warns:
08:34:46.896
Non-Fabric mod JAR at "C:\Users\Admin\AppData\Roaming.minecraft\mods\Xaeros_Minimap_21.8.2_Forge_1.16.5.jar", ignoring
08:34:46.928
The mod "cardinal-components-base" contains invalid entries in its mod json:

• Unsupported root entry "side" at line 8 column 11
  08:34:46.929
  The mod "cardinal-components-entity" contains invalid entries in its mod json:
• Unsupported root entry "side" at line 8 column 11
  08:35:31.805
  Ambiguity between arguments [teleport, destination] and [teleport, targets] with inputs: [Player, 0123, @e, dd12be42-52a9-4a91-a8a1-11c01849e498]
  08:35:31.806
  Ambiguity between arguments [teleport, location] and [teleport, destination] with inputs: [0.1 -0.5 .9, 0 0 0]
  08:35:31.808
  Ambiguity between arguments [teleport, location] and [teleport, targets] with inputs: [0.1 -0.5 .9, 0 0 0]
  08:35:31.809
  Ambiguity between arguments [teleport, targets] and [teleport, destination] with inputs: [Player, 0123, dd12be42-52a9-4a91-a8a1-11c01849e498]
  08:35:31.810
  Ambiguity between arguments [teleport, targets, location] and [teleport, targets, destination] with inputs: [0.1 -0.5 .9, 0 0 0]
  08:35:40.218
  Ambiguity between arguments [teleport, destination] and [teleport, targets] with inputs: [Player, 0123, @e, dd12be42-52a9-4a91-a8a1-11c01849e498]
  08:35:40.219
  Ambiguity between arguments [teleport, location] and [teleport, destination] with inputs: [0.1 -0.5 .9, 0 0 0]
  08:35:40.220
  Ambiguity between arguments [teleport, location] and [teleport, targets] with inputs: [0.1 -0.5 .9, 0 0 0]
  08:35:40.220
  Ambiguity between arguments [teleport, targets] and [teleport, destination] with inputs: [Player, 0123, dd12be42-52a9-4a91-a8a1-11c01849e498]
  08:35:40.221
  Ambiguity between arguments [teleport, targets, location] and [teleport, targets, destination] with inputs: [0.1 -0.5 .9,

Errors:
08:35:04.491
No data fixer registered for byg:boat
There were no fatals.

As for the rest of the info, it's too big to copy down and paste here.
I hope with this information you can find the issue.

That's... even more bizarre because they all use the same logic. Like, literally. They all use the exact same class.

Oh, also. R itself shouldn't be a requirement. It's just spacebar, like an elytra, and holding W to give yourself the speed. R is just my sprint key.

Yeah, just tried every set of wings. They all work the same with the list of mods you've given me. I'm not sure what the problem is :/

Does it still happen with just Icarus installed?

So I just installed all the same mods that you have, but it's working fine for me? Is there another mod you're leaving out, like Optifine, or maybe you're activating the wings wrong? Or maybe you don't have any hunger and that's why it's not working?

So I just installed all the same mods that you have, but it's working fine for me? Is there another mod you're leaving out, like Optifine, or maybe you're activating the wings wrong? Or maybe you don't have any hunger and that's why it's not working?

No that is all the mods I have installed currently. My hunger was full when using them and if I'm correct it's double jump/R to activate them. No idea what is causing it since they seem to become invalid when I re-equip them after already putting them on.

EDIT: After doing some further testing it seems this only happens with the dragon wings. The other wings work fine.

Yeah, just tried every set of wings. They all work the same with the list of mods you've given me. I'm not sure what the problem is :/

Does it still happen with just Icarus installed?

Seems like it does. I used the gray and black dragon wings when testing but other than that I have no idea whats causing the issue.

Seems like it does. I used the gray and black dragon wings when testing but other than that I have no idea whats causing the issue.

Then I have no idea what the issue is. I'm not getting this at all when I test it myself, and the logs aren't showing anything weird. Hate to do this, but I'm just gonna close this and tag is as wontfix because I don't think there's anything I can do.