Can an estate take a charitable donations deduction for the personal items (clothing, furniture, etc.) of the estate that were donated?

An estate can take a deduction for charitable donations, assuming there is income to deduct against.  And, the value of the deduction will generally be limited to the cost basis of the donor (the price the person paid for the items) and not their fair market value.  See publication 526 under "giving property that has increased in value."

The fiduciary of the estate must be given the express authority to make the donation in the governing instrument (in this instance, the will) and the donation must be made from gross income (not from corpus) so this particular charitable donation probably won't qualify for a deduction.

The proper way to handle this would be to distribute the items to the beneficiary(ies) who, in turn, would donate the items and take the deduction on individual income tax return(s).