Like-kind exchanges no longer apply to anything except real property. In other words a car is not considered real property. (IRS Publication 544, page 11)
The basis of the old car and the insurance proceeds will determine whether you have a gain or a loss on the old car. This will not affect the basis of the new car since there was no trade-in for the old car. Follow the instructions above to determine and report gain or loss on the business portion only of your vehicle.
If you are able to itemize deductions, the personal portion of the vehicle may be able to be used as a casualty on your Schedule A. A casualty loss must be greater than 10% of your adjusted gross income. If the loss is greater than 10% of your AGI, then you can add that difference to the rest of your itemized deductions to see if it is more than your standard deduction.
As pointed out by @Mike9241 the personal loss must have been associated with a federally declared disaster area or a Ponzi Scheme under the Tax Cuts and Jobs Act (TCJA) from 2018-2015. If not, there is no personal loss to consider.
{Edited: 01/23/2023 | 9:40PM}
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