Except for cars, boats, and airplanes (which are covered under a special rule), the value of a donation is never determined by the amount of benefit the charity gets, but is the fair market value of the property. Generally, that means what you could get for it if you sold it to a stranger at a thrift store, garage sale or auction. The amount of benefit does not enter into it -- for example, in my city, Goodwill automatically recycles any computer older than a certain date because it is too much trouble to figure out if it works, clean it up, etc. A computer that you could sell for $100 on Craigslist is worth nothing to Goodwill but you still get a market value deduction. Or, imagine the chaos when you donate clothes, and then you got a letter a year later saying "no one bought your clothes so we sold them to a textile recycler for 25 cents a pound." But the donation is the fair market value of the items no matter how the charity uses them.
Also, please read the other answers and comments carefully -- the Patel case is the law of the land for now, and that says that donation of a structure to a VFD for training is never deductible. The reasoning is that you only loan them the use of your property, and you can't donate the value of the temporary use of property. There may be room to challenge the ruling, but that would require claiming the deduction, getting audited, and going to tax court.
Finally, also be aware that any non-cash donation of more than $5000 requires an appraisal, and the filing of a special tax form signed by the appraiser and by the donee organization. So if you do decide to claim the donation you will need a written appraisal of the structure before the burn, to prove the value of the donation that you claim. And it won't be enough to say that the amount you saved on demolition costs is negligible. You have to prove it. The IRS will likely say that, no matter how much you had to pay for site prep and demolition after the burn, you would have had to pay more for demolition without the burn. You can't rebut that with your say-so, you would need some kind of documentation.
