Can I claim mileage for attending a 51 day training academy, that was required by my employer after I was hired as a Firefighter

Yes, this is a business expense. You will include this in your itemized deductions on Schedule A. 

Here is how to enter it in TurboTax Online

To enter in TurboTax Deluxe

Go to Deductions & Credits

Scroll to Job Expenses for W-2 Income

TurboTax will walk you through all your possible deductions for this training and any other expenses you have.

These expenses must be more than 2% of your AGI to be deductible, so you may not see a difference in your calculations. 

For more information, follow these links: 

https://www.irs.gov/taxtopics/tc511