Is there a way to save an existing gradient used in a slide show to the gradient list?
Please clarify: What 'gradient' did you meant?
Did you meant the background colorize feature of the graphical objects? If the ansver is 'YES': it works in my AOO 4.1.3 portalbe version, and in my LibreOffice 4.4.7 verion.
You must SAVE the created custom gradients to the default gradients list if you want use it in the future for other documents.
Use the 'Add' button to create and name of a new custom gradient, then adjust it, and then use the 'Save' icon on the dialog box.