Anthony, you are certainly brave to tackle this.
One of the big concerns is companies not paying tax because they are increasing market share and value while not making profits (Amazon could continue doing this until goes out of business). A VAT (as opposed to sales tax that applies only at retail) can take care of this because companies buy stuff. It could replace corporate tax and also possibly traditional income tax.
This, as you say amounts to a flat tax, but can be in harmony with a generous base income for all adults. A cut off point can be made but needs to be pretty high.
Capital gains? Not sure. Probably needs retaining.
Many thanks