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 computer visit the business page and select the "Add a Button" option underneath the cover photo:
You'll be asked to select a button — choose "Book Now", and click Next.
Now choose Link to Website, and enter the link to your Client's Scheduling Page, then click Save and click Finish:
Check out your Facebook page on the Facebook mobile app. The button should show at the top of your business page!