You'd wear down your teeth grinding this stuff, so you swallow it in chunks. Wiggle them around with the gemstones till they're pulverized.
10 seconds sound clip from the The Flight of Dragons movie soundboard.
You can hear this line at 00:42:31.290 in the Blu-ray version of the movie.
Quote context
[...]
- Hurry now, before we devour you!
- Now swallow them down. Not all the way, let them find your craw.
- Never had diamonds in your craw?
- They help grind up the white fire rock when you eat it.
- A puny man word if I ever heard it. Eat!
- It's like birds use grit to grind seeds.
- Yeah, but don't talk with your mouth full.
- What's all this to do with flying?
- It makes the fire in your belly that gives you lift.
- What? You got fire inside you when you go up. That's all you need to know.
[...]