A CO2 tax and rebate is progressive. The poorest people would receive more back in a rebate than they pay. But the biggest CO2 users would pay way more than they receive back.
While I generally like CO2 tax/rebate/cap-and-trade systems: given how inefficient and polluting many low-cost techs are... not sure I can agree with that, particularly on the small scale down to individual people. Individuals have the least agency on decisions like this, since they have next to no purchasing power. Though we are talking about bitcoin, which does raise the technical/money base-level a fair bit.
Wouldn't it be easiest to tax some of the raw materials that go into fuel production, rather than tracking every fuel use? In that case, the CO2 tax will naturally fall equally to everyone, including individual people. The rebate is just there to cancel out the effect of an inherently regressive but technically convenient way of doing things.
That's generally the idea of a flat tax, yeah. Tax everything at point-of-collection/creation (e.g. "you cut down a tree" or "you burned a log") or point-of-import (likely offset for similar taxes collected by the origin country), and there's no need to track anything beyond that point. E.g. re-use or re-selling is (CO2-)tax-free because it doesn't change the net input/output of the whole system.
Which rarely happens in practice, and we're so far from accurately taxing all these processes that it isn't even a dream of a dream. It's mostly tackling big targets, since that's where a ton of the impact-per-dollar-and-per-outrage can be found.