The IRS allows you to deduct "ordinary and necessary business expenses,"
https://www.irs.gov/forms-pubs/about-publication-334
Separately, the IRS has specific rules and regulations for deducting car expenses, and they are divided into two categories. "Travel" is when you need to travel away from your tax home (the area where you make most of your money) on business for overnight or longer. "Transportation" is when you drive locally for business reasons. These are both described in publication 463.
https://www.irs.gov/forms-pubs/about-publication-463
None of the rules for car use contemplate using your car as a "stage" for a performance, rather than as transportation. So this is something of an unknown area.
My answer would be "no". First, filming yourself while driving is extremely dangerous, and in some locations is illegal, and illegal activities are never allowed as deductible business expenses. Second, filming yourself is using the car as a backdrop, not for transportation. Any car expenses (gas, insurance, etc.) are related to the transportation function, not the backdrop function, and so are not "ordinary and necessary" expenses for the backdrop function.
But this is just my interpretation.
