You set the sales tax rate flatly, and then settle the disproportional tax levy on the annual filing where you can have a simple, clean, discount rate based on reported income.
This is clean, simple, and inevitably fair. It is NOT perfect, but a hell of a lot better than the mess we've got right now.
Poorer folks will pay more in real terms over the course of the year, but they'll get a check back each year from the government to reimburse them. That check could include an inflation calculation, etc... to offset the initial outlay.
You can toy with the idea of setting up sales tax exempt items (such as food), but then you start to make the whole thing more complicated, and prone to manipulation.
I conduct my personal and professional life by the KISS model. I think our government can learn from it.