And your actions do have an effect: by providing an example to others, making it more likely they too will participate; and economic, by reducing the income generated from the activity.
Silent Spring was written by a Rachel Carson and had real impact. However, her personal lifestyle was irrelevant.
PS: As to someone going first, that is not an issue when say a state adds a sales tax. In such cases the first person to pay the tax is a sign that it's already in place.
No one said your singular vote (with your wallet) would change everything. But just like voting you help push things in the right direction. And you can, with additional effort, influence more people to vote the same way as you.
Now consider the impact of the right 40,000 people voting differently in the 2016 US Presidential elections. All sorts of things would look very different, including action being taken to fight climate change.
One person can make a difference, by influencing others. But you have to be smart about it. You can't just decide to fly less, and then declare that you're making a difference because one person can make a difference.
Rich people flying less won't do anything to convince governments to fight climate change, so what's the point?