If flight tickets are priced so that they take into account the correct price of carbon (finding this is no simple task in itself), then emissions will be reduced by an appropriate level, as consumers will not value the flight more than the new cost, and the industry will have an interest in cutting emissions to save money. Until then, any voluntary "compensation" scheme is negligible in effect. But yes, the last decades of insanely cheap flights can't go on, atleast not with the same amount of emissions from it.
"Flyskam" has been mentioned in Norway as well, but only as a Swedish "cultural export". Moralism like this is common in politics, but not useful for actually reducing emissions.