@Timbeck2
I am a CPA but I do not practice. So take any of what I say with a grain of salt and please don't get my license yanked. I am speaking as SGOTI.
Your participation in Pilots N Paws falls under IRS Publication 526 as providing a service to/for a charity. You may be reimbursed for out of pocket expenses in connection with giving that service. Transportation costs are allowed to a certain extent. They get very specific about car expenses and say this:
Car expenses. You can deduct as a charitable contribution any unreimbursed out-of-pocket expenses, such as the cost of gas and oil, directly related to the use of your car in giving services to a charitable organization. You can't deduct general repair and maintenance expenses, depreciation, registration fees, or the costs of tires or insurance. If you don't want to deduct your actual expenses, you can use a standard mileage rate of 14 cents a mile to figure your contribution. You can deduct parking fees and tolls whether you use your actual expenses or the standard mileage rate. You must keep reliable written records of your car expenses. For more information, see Car expenses under Substantiation Requirements, later.
Obviously you want to know about airplane expenses. They would follow in the same spirit as the car expenses. However, I am not aware of a standard airplane rate like they have for cars above. Since flying airplanes is not as common, they don't have a standard for it. The $1.27 that you found is for allowing government employees to use personal aircraft to conduct federal business and to deduct it like the standard mileage rate for cars when getting reimbursed. The GSA rates have nothing to do with the IRS so they do not apply to charitable giving.
So like the advice given by others above, you really can only deduct direct expenses for the trip you take - which is essentially fuel, oil and landing fees. You cannot use an operating rate because that would include maintenance, which is specifically not allowable under the car rule.
You then must keep records of what expenses you incurred while performing your service for the charity. Sticking with the spirit of car expenses the publication says:
"If you claim expenses directly related to use of your car in giving services to a qualified organization, you must keep reliable written records of your expenses. Whether your records are considered reliable depends on all the facts and circumstances. Generally, they may be considered reliable if you made them regularly and at or near the time you had the expenses. For example, your records might show the name of the organization you were serving and the dates you used your car for a charitable purpose. If you use the standard mileage rate of 14 cents a mile, your records must show the miles you drove your car for the charitable purpose. If you deduct your actual expenses, your records must show the costs of operating the car that are directly related to a charitable purpose."
Now I am sure someone will come along and tell us how he has a friend that deducts his annual and hangar because they do PNP flights once a month. I doubt that would ever stand up to an audit and they are just playing with fire.
Anyway, hope that was helpful.
Edit: added link to IRS Pub 526
https://www.irs.gov/pub/irs-pdf/p526.pdf