If exporting via email is already enabled in the NIH Toolbox app, but the app is not allowing you to export via email, it may be an issue with your iPad's email settings. Try sending an email from another app to test this, such as MindList or Merriam Webster, which can be downloaded from the App Store. After installation, tap the account or settings (gear icon) button, and locate a Contact Support option. When an email draft pops up, enter any email and see if the Send arrow is enabled (it is not necessary to actually send an email).
If the button is not getting enabled, please discuss with your IT. It is possible that email usage is not allowed by an MDM Profile on the device.