I'm not disagreeing with the need to look after the environment. But a progressive tax is one based on ability to pay. Therefore tax based on the number of flights would hit the least well off hardest, and would be completely retrogressive.
Sorry to disagree but a tax on flying based on the number of flights taken by an individual would be decidedly progressive. A tax based on the number of flights would not hit the least wealthy hardest but those with the greatest ability to pay - the wealthiest! There are various figures out there on the interweb but one of the least controversial is that 70% of flights in the UK are taken by 15% of the population. If, therefore, a tax structure was arrived at in which, perhaps, no tax was incurred for the first two flights, 10% for the next two flights, 25% incurred for the next two flights, 50% for... you get the drift. This would be progressive and, I suspect, a powerful disincentive to those who fly a lot to continue with their damaging activity.
Political decision-making changes people's behaviour. All we need is a government with the testicles to propose and enact such policies!