Branded icons and illustrations

There are a lot of options, so I think we might need some more specificity.

If you want to create a template, you'll need to edit your themes, master slides, and player, then "save as" a template (open the drop down on the file type).

If you have a set of icons and illustrations, you can import them; but the obviousness of that solution I think is begging a question. Do you want to see more integration of your custom media? There is the media library tool, where you can control media across your entire project. 

Articulate is working on some Team media tools, but they aren't out yet.

Another problem is that the toolset for working with SVGs as icons isn't great. I highly recommend the workflow where you import vectors to PowerPoint, change them to PowerPoint graphics, then import the PowerPoint to Storyline, then ungroup them, thus giving you access to the vectors in a way that responds to theme colors.

If you have a robust set of icons, I would import them once as a batch through PowerPoint on a single slide, separate and organize them into their component parts in Storyline, then save that as a template that you can open and copy-paste/duplicate your icons as needed from that initial slide. You can even hide that slide from the menu during publication if you don't want to delete it in case of future edits.