How can I get a rental car approved for attending the Battle Staff NCO Course at FT Indiantown Gap?

Training dollars can only pay for a rental if it is a necessity to get between billeting, training and chow in a timely manner (required to complete training; doesn't matter where the store, barber or church is).
Your state's G3 publishes your order and approves your DTS for school. Typically the state's G3 and/or USPFO business practice is to require an ETP approved by G3 for a rental for school. The ETP must demonstrate the distances between billeting, training and DFAC.
In our state, if any one of those three distances exceeds 1.5 miles, we approve one rental car for up to four Soldiers attending that class.
If billeting is not available and students must get lodging off-post, no ETP is required for the rental car.

In your case, the welcome letter says "not co-located" and "up to 10 miles".
And the letter states that the trip for lunch will be 5 miles round trip.
However, the billeting and the only DFAC shown are co-located, and the classroom is 0.9 miles from there.
They need to provide a map or street address showing a DFAC further away, or you might not get a rental approved.

Also, the letter mentions civilian internet access reimbursement. Don't claim that on your DTS, as the welcome letter clearly states that the class-issued laptops cannot access the civ internet, and can only be used in the school building, hence the civ internet access is not required (or even possible) to complete training and is not reimbursable.

It would need to be checked Approved for Rental on the RFO

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