I would add ONE(1) deduction, a personal deduction for each individual covered by the return.  Set this deduction so that a family of four(4) at the poverty level is tax free.
Flat tax or progressive, I don't care, but one tax table for everyone (i.e. no married, single, or married filing separately).  Get government out of the marriage business; stop using tax code for social engineering. For an extended family, add all the income, subtract the individual deductions, and pay tax on the balance.

Eliminate corporate income tax!  They're a pass through, paid by customers. Need $s for taxes, raise prices. Congress uses this sleight-of-hand to fool the public.

I go back & forth on how to treat long term capital gains. If you consider them ordinary income, it makes no difference with a flat tax.  But with a progressive tax, they push you into a higher tax bracket.  This would induce investors to focus on short term ROI, which is bad for growth.