My company reimburses (and grosses up) for tuition above the nontaxable amount. Should the amount above $5250 be taxed at my highest Federal Tax rate so I avoid taxes?

Tuition reimbursement above the non taxable amount is included in box 1 of your form W-2. This excess of the non taxable amount is taxed at the IRS table rates. So, in the end, it is taxed at your marginal tax rate (which is the highest tax bracket for your taxable income.

Q.  Should the amount above $5250 be taxed at my highest Federal Tax rate?

A.  Yes.

Q.  So, how do  I avoid taxes?

A. Since that  money was taxed  (the amount above $5250), it is considered your money and not employer tax free reimbursement. And it was used to pay qualified educational expenses (tuition & fees), so you may use that amount to calculate and claim a tuition credit.  You may not count the $5250 of tax free money to calculate the credit.