Sales tax would be the only conventional tax in the scheme proposed. So it would need to be as high as needed to fit the public government spending. In some EU countries that would be above 50%, in the US may be roughly 40%. That may seem like a lot but averaged it would be the same than the average tax payer paid before, except more evenly distributed so likely median tax payer would be benefited.

UBI by itself is progressive, a simple flat UBI creates a progressive effective rate. You can tweak the numbers to obtain your desired target tax curve; increasing or decreasing UBI, having different VATs for different products. As John Von Neumann said, "with 3 parameters I can draw an elephant and with 4 I can make it wiggle its trunk". There is enough free parameters to make the taxation more or less progressive.

I'm not prescribing those details because I think there should be ample room for fine-tuning. What size government spending should have in an economy and how progressive should a tax system be are questions that different countries have answered differently and you find success and failure all across the spectrum. So I consider it a transversal issue.

My focus is on efficiency, resiliency to abuses/gameability and economic incentives.

I admire the proposed simplicity (and agree that setting the levels can largely mitigate any concerns of regressive nature [especially as compared to today]).

My concern under a sales-tax only system is that politicians also like to be seen as aiding employment and a sales-tax only system does not seem as supportive of employment as today's system where employment expenses are offset in part by their tax deductibility. No one goes out and employs someone for $100 to save $20 on taxes (still -$80), but I still employ more people when it costs me $80 than when it costs me $100 to do so. In that regard a VAT is superior to a straight sales-tax.