Is there anything available in the Box API equivalent to this Dropbox Saver?
https://www.dropbox.com/developers/dropins/saver
I want users to be able to pick a specific folder to upload to.
If not is there any other way to achieve this?
Check out the Box File Picker. This will handle authentication and folder selection. It doesn't do the 'upload file to folder' part of the Dropbox Saver. If that's your ultimate goal you may need to add a bit of additional code.