Can something that is one-of-a-kind be "rare"?

Is rare an appropriate descriptor for something that is one-of-a-kind?

No. Something that is one-of-a-kind is unique. Something that is uncommon but not unique is rare.

• The Mona Lisa is unique.
• Gold is rare on our planet.
• A custom-made guitar is unique, built to particular specifications and reflecting the capabilities of its maker.
• Guitars that have been played by Jimi Hendrix are rare.

Yes it is reasonable to apply 'rare' to one of a kind. For two reasons.

First is that it is reasonable to consider that "unique" is just an extreme form of 'rare'. But being an extreme form of rare does not stop it being rare. If there were only three of something it would be rare, or if there were two - therefore it does not make sense to everybody that something even rarer - there is only one - stops being called rare.

Secondly unique things can be rare as a category. If a Craftsman makes handcrafted decorations then each is unique. If he makes many millions, each one can still be unique while as a category they are common. If he makes only a few then they would be rare (while each one is still unique).