The IRS took in roughly $1 trillion in individual tax returns(versus corporate) in 2003. That means you need to cut $500 billion out of the budget to support a 20% flat tax. $493.5 billion to go, assuming you cut all the programs you listed to zero.
I agree that there are private schools that cater only to handicapped kids. I worked at one around here, Woods Services, when I was in high school. There might be 100 on
this page. That's not enough capacity, nor is there one available to every child with special needs.