Probably not.  This type of expense used to be deductible (subject to 2% of your AGI and itemized deduction thresholds), but, because of the Tax Cuts and Jobs Act, unreimbursed employee expenses are no longer a deductible expense.  The only way these expenses are deductible is if you are self-employed, which you as a teacher are not considered to be.

If you are a volunteer coach (completely unpaid for that work), you may write off the mileage as a charitable contribution.  But if you are paid to coach there is no write-off for this.

Instead, you may talk to the school board if they have a provision to claim reimbursement for these expenses.  Any reimbursement is tax-free to you, but is a deductible expense on their entity's return.