Deduct mileage for FFA project

It depends. As you indicated it is not a business (reported on Schedule C), rather a hobby and/or a learning experience. Expenses for a hobby are not allowed on the tax return,

You can decide if it is hobby or business income.  This IRS link will help you: Business or Hobby?

Key elements:

1. A hobby requires you to report the income you received and under the current tax law, Tax Cuts and Jobs Act (TCJA), no expenses are allowed to be used to reduce the money collected even if you itemize deductions.
2. A business allows you to deduct the costs necessary to obtain the income.  The law explains that 'you must be engaged in the activity to produce a profit'.  The test under IRS tax law is that you must show a profit three out of every five consecutive years to be considered a business.

If it is a hobby, then you would report the income using the steps below. Other Miscellaneous Income:

1. Go to the Wages and Income  section of TurboTax
2. Scroll to  Less Common Income > Select  Miscellaneous Income, 1099-A, 1099-C
3. Select Hobby Income and Expense > Enter the income

It does require Schedule 1, but not Schedule C or F.

Because it is not a business, I don't think you can use the Standard Mileage Rate.  But if you can reasonably come with up actual expenses for vehicle usage, I would think that would be fine.