They can do that with other taxes. I don't see the point here.

If we take a flat percentage of the spending and give everyone the same fixed amount, poorer people will profit more than rich people.

If you take a flat percentage small enough that poor people can afford it it's not even going to be close to enough for UBI. Sure poor people will profit more (if you assume they have a smaller CO2 footprint), but only at a scale of like a couple bucks.