1. The three-year restriction on disposing of donated property.
There is a real IRS rule involving donated property and a three-year period. However, it is not a blanket prohibition against selling or disposing of donated property.
Under Internal Revenue Code Section 6050L, certain charitable organizations must report dispositions of qualifying donated property within three years using IRS Form 8282.
Reporting a sale is not the same thing as prohibiting a sale.
2. The claim that the IRS prohibits disclosure.
This is the part that concerns me more.
I'm not aware of a general IRS rule that prohibits a charitable organization from disclosing information about donated collectibles for three years.
A private Deed of Gift could contain confidentiality provisions, but that would be a contractual restriction, not necessarily an IRS restriction.
What the IRS actually says
The IRS confirms that organizations can dispose of qualifying donated property within three years, subject to reporting requirements and possible tax consequences for the donor.

Internal Revenue Service
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Is there any current law that says you cant disclose a donation
No. There is no general federal law or IRS regulation that prohibits a charitable organization from disclosing that it received a donation, identifying the donated property, or publishing an inventory of that property.

That applies to organizations such as the Casino Collectibles Association (CCA), assuming it is operating as a tax-exempt charitable organization.

There are important distinctions between three things:

Disclosing the donation: Generally permitted. An organization can announce that it received a collection and describe its contents.

Disclosing the donor's identity: Certain donor information is protected from public disclosure in IRS filings. That does not mean the organization is prohibited from voluntarily acknowledging a donor in every circumstance.

Selling donated property: IRS rules can require reporting when certain donated property is sold within three years. That is not a blanket prohibition against selling it.