This is so hard to do in Power Apps. Currently other than a combobox, there is no true multi-select control in Power Apps. Combo boxes are clunky to use and have limited display options. Radio button controls only allow a single selection and you would have to add multiple check boxes to simulate a multi-select control.
This precludes using data from an external list to populate the controls (except the combobox). The capability of multiple selections being passed to SharePoint or other repositories and being used to control other fields and choices already exists with the Combo box, so it seems like the same functionality should be able to be used in a true multi-select checkbox control.