Having been faced with the same problem and seeing as how Adobe have steadfastly not answered the query for 10 years (the oldest reference to this query that I found, and unanswered then too), I have created a workaround that seems to work.
Steps:
1. Go to where the Custom Stamps palette contents are stored on your computer. In my case (on a Mac OS X 10.14), it is in
~/Library/Application\ Support/Adobe/Acrobat/DC/Stamps. Each of the files there contains the stamps used in each Custom Stamps category.
2. They are named with a "random" string but you can see the contents in a preview or with a PDF viewer. Open the relevant file in Acrobat Pro.
3. In Acrobat Pro, go to Organize Pages. You will see the stamps on individual pages, in the order they show in the Stamps palette. If you haven't already, close the Stamps palette.
4. In Organize Pages, drag each page (the stamp) into the order you want them to be shown on the Stamps palette.
5. Close Organize Pages. Save the file with the same name.
6. Quit Acrobat Pro, then restart the application. Open the Stamps palette. The stamps should now be in the order you want.
AdChoices