How do I check whether I retained copyright for a figure in a paper from ten years ago?
Unless the paper is open access, the publisher usually holds the copyright. This can be seen in the imprint on the first page of the paper. If it says "(c) the publisher" then the publisher holds the copyright, while if it says "(c) the authors" then it's the authors who do.

In the case of your paper though, the Royal Society's plagiarism, copyright and intellectual property page says


  Authors of non open-access papers retain the copyright, but grant the Royal Society the exclusive right to edit, adapt, translate, publish, reproduce, distribute and display the article in printed, electronic or any other medium and format.


I'm no lawyer, but I take this to mean that while you cannot distribute the paper in its final form, you can distribute a single figure.