The Facebook App for Acuity doesn't show in the mobile Facebook App. The trick is to add a "Call to Action" button to link to the client scheduling page. The steps to setting that up are:
From a desktop computer, visit the business page and select the "Create Call to Action" option at the top of the page.
It'll ask you to "Choose Button", select "Book Now". In the "Website" field, enter the link to your Client's Scheduling Page. Choose "No" for the "Set up link to an app?" question. Double-check the Client's Scheduling Page link show in the iPhone and Android tabs as well. When done, choose "Create".
Check out your Facebook page on the Facebook mobile app. The button should show at the top of your business page!