Depends on what you mean by "hourly employee". If his yearly pay is reported on an IRS W-2 form, then no, you cannot deduct any vehicle expense or mileage. If you are a regular W-2 employee, you are no longer (effective 2018) allowed to deduct mileage and other job expenses. Even when you were allowed to, it was only an itemized deduction subject to the 2% of AGI threshold.
Talk to your employer about getting reimbursed. The employer is allowed to deduct mileage reimbursement to employees. When done right, the reimbursement is not taxable income to you.
If his pay is reported on a form 1099 (usually a 1099-NEC), then yes, you can claim the full mileage deduction rate, This is because he is considered by the IRS to be self employed.
