Jet-A1 is already untaxed in most of the world, so if the price of oil quintuples so will the price of Jet-A1 (more or less).
Jet A1 as well as Avgas is not taxed for commercial international operations, private ops are usually fully taxed. Another example to show that private airplane users are regarded as milking cows with too much money to spend.
Frankly, the injustice of this is striking. Either it is taxed for everyone or noone. The tax levied on private ops fuel does really not bring anything of note into the government's kitty, it's purely a "luxury tax" levied by people who think all private planes are multi million jets. They should really sit in a 1960ties PA28 once to see how wrong they are.
Rather than taxing only private ops but with a 70-100% tax, if everyone was taxed say 2-5% it would actually bring in some profit while it would stop to punish those with the least potential. But then again, that would be against the Eurocommunist dogma of punishing private property.