As mentioned here: How can I start the Accessibility Settings Page of my APP in Android? I can open my app Accessibility Settings directly with this code:
Intent
It work below kitkat 4.4 only. This vulnerability issue is resolve in 4.4 and above. Accessibility permission is one of the crucial permission and android not allow you to directly access that app page as of now there is only way to open Accessibility service is
startActivity(new Intent(android.provider.Settings.ACTION_ACCESSIBILITY_SETTINGS))
And then user can choose your app if he want to allow permission