Even some of his climate stuff annoys me.
But, it's highly likely that if you ranked the whole human race on how much they'd done to reduce climate change, he may well be at the top.
So if it's about "doing his share" then he's probably doing okay.
But regardless, I don't want people to stop flying, I want them to stop releasing fossil C02 in the air because it's inefficient. Inefficiencies on an individual scale don't matter, inefficiencies on a civilization wide scale add up quickly.
I don't see how flying, or doing any other rich person thing, reduces his credibility. Unless you believe dealing with climate change is going to make us all poorer, which it isn't.
If you're really all about hating rich people, then there's lots of "climate justice" projects aiming to help poor people and carbon taxes that replace regressive taxes would be a good thing to champion.