Since Android apps are now available on Chromebooks via ARC++ (Android Runtime for Chrome 2nd version), developers coming from a traditional File storage background will have to make sure their apps conform to take advantage of how to access the SD card.
The Chromium team has implemented USB On-The-Go access for the SD card on ChromeOS 62 (Chromium M-61?) or higher. What this means is that developers who expect their apps to work with the SD card as if it was under the battery in their phone will be disappointed. This is due to the fact that a 'hot swappable' SD card such as those found on a Chromebook isn't considered Adaptable Storage by the Android Framework.
Additionally if you want to use the MediaStore APIs to access it, you are still out of luck as the Android Framework does not support access to removable hardware. The Chromium team is aware and considering options:
So what to do?
See this Commonware's post on Removable Storage for further details.
Originally a StackOverflow answer: https://stackoverflow.com/a/44123748/295004