So, for instance, Elon Musk's private jet is estimated to have emitted 2,112 tons in 2022. Elon would have to pay a $400,000 carbon tax.
Ideally these taxes would flow through fuel, but that presents some challenges, since planes can re-fuel in jurisdictions without those taxes, although that's certainly harder to do in the United States. I think in the US, it might be hard enough to do that that just taxing the aviation fuel is fine.