When moving the dyed elytra (i.e. by sneaking or gliding), the color will flicker between the default gray and the color of choice. It doesn't flicker while standing still, however. I am using Quark version r1.5-130 for Minecraft 1.12.2, along with some other mods. The issues occurs both with and without Optifine installed.

Would one of those mods happen to be Colytra?

Nope. Colytra isn't installed.

Can I get a mod list?

The issue is with Galacticraft. I was confident as soon as read that list, but I tested just so I wasn't wrong on the internet. This likely isn't fixable because Galacticraft heavily messes with how things render on the player model.

Ah damn. Not much I can do in that case.

Yep, once I'm not dying of school work, like tomorrow.

Managed to squeeze this out before going to bed, enjoy.

I've been running a small profile through the Twitch/Curse launcher. I recently took out IC2 Experimental, Galacticraft, and Extra Planets, and replaced them with just IC2 Classic. I hadn't checked the Elytras since, but after checking just now the issue seems fixed! I think one of those three mods was causing the issue.

In case you're curious, here's the current mods list. The old mod list from when I posted the issue is the same, except for the changes mentioned above.