If audited, you bear the burden of proving your expenses. So in strictest terms, if you don't have records of your mileage, you can't deduct anything. Your records must be contemporaneous—made close enough in time to the actual trips that you can rely on your memory to be accurate. A daily diary is best. There are smartphone apps for tracking milage, and some more expenses GPS units will remember your trips for you.
Beyond that, what answer do you think anyone can give? Maybe amazon has a record of your stops, that you could put in google maps to put together an estimate. Maybe you guess that your average is so many miles per day. If you have records of oil changes and other car maintenance, maybe you can figure out the average miles per month you drove before becoming an Amazon driver, and the average number of miles per month after, and the increase is probably your work miles.
But if you don't have records, or your records are obviously cobbled together after the fact from memory, estimates and guesses, you lose the deduction if audited.
Good luck.
