Our development team will be working on a Screen Recording feature for early 2019. In the mean time there are a lot of free solutions our providers use.
Screencastify is a free chrome plugin.
If you use a Mac you can use Quicktime to record.
You can record a session with Camtasia that works in parallel with doxy.me. Then you can save it to your computer or local drive. Here's the link to a free trial of Camtasia.