I have the same issue and would like to know if there's a way to do this.
No answers about how to do this?
I think it would be quite useful for application developers if Apple provides a way to do this
The only way for an application to request permission to use Accessibility features is with the API provided by Apple, namely AXIsProcessTrustedWithOptions.
What my company's software does is, during the postinstallation phase of installing, launch any of our applications that require Accessibility permissions and have them call AXIsProcessTrustedWithOptions.
Unfortuantely it inundates the user with multiple windows asking to grant apps permission. Furthermore our installer installs a kernel extension so starting with 10.14 there's also a dialog asking for permission for the kext to load, and in 10.15 it will require a reboot as well.
There is horrible UX. Unfortunately Apple doesn't provide us any way of doing anything different. It's quite unfortunate, and a lot of it strikes me as pointless.
I would love Apple to give us a method of granting these sorts of permission during the installation process in a way that's easy for the user to handle, but don't hold your breath. In the future I expect we'll see more features get locked away behind permissions dialogs resulting in further UX degredations, and I don't expect we'll see any new features that alleviates this problem.