There are several threads on Pilots-n-Paws forum. But there here is a link (from that forum) from a law firm about deducting expenses as a charitable donation.
https://www.pilotsnpaws.org/forum/download/file.php?id=3833
According to them, you CANNOT deduct fixed costs (annual, hangar rent, insurance). Only fuel and oil, pilot fees (landing/ramp/parking), rental costs, additional costs for insurance for this activity.
"No Charitable Deduction for Fixed Costs of Flights for Charitable Purposes
While the FAA now appears to permit aircraft operators to perform some charitable flights and take the associated tax deduction, the IRS only allows a charitable deduction for variable costs of transportation for charitable purposes.8 “Only those expenditures incurred for operation, maintenance, and repair, which are directly attributable to the use of such aircraft” on a charitable flight can qualify as charitable deductions. Examples of costs that could be “directly attributable” to a charitable flight include (a) the cost of fuel and oil for the flight, (b) pilot fees incurred solely for the flight, (c) rental charges for an aircraft used only for the flight, and (d) extra liability insurance incurred only for the flight."