If you volunteer for a non-profit organization, the amount you can deduct for mileage spent on their behalf is 17 cents per mile, much lower than the standard rate for employees and self-employed.
If you volunteer for a for-profit company you can't take a charity deduction for your mileage.
Whether you volunteer for a company or a non-profit, you do not need to report their reimbursement of your expenses as taxable income as long as the reimbursement is "accountable." That means you have to submit proof in the form of expense records, a mileage diary, trip reports, or something similar. They can reimburse you up to your actual cost and it is not taxable income to you. If the reimbursement is not accountable (such as, they pay you a stipend regardless of how many miles you travel) then you are an employee or contract worker and the payments are taxable.
Since you are not an employee, you can't take an additional tax deduction for the difference between the reimbursement and the standard rate. You just get what you get. (If you are volunteering for a qualified non-profit and the reimbursement is less than 17 cents, you can claim that difference as a donation to charity.)
