I used to have this problem but I found a solution, so just decided to post it here just in case someone else needs it.
How to launch the native installer app to install an apk?
Many posts have the solution as below:
Intent intent = new Intent(Intent.ACTION_VIEW);
intent.setDataAndType(Uri.parse(path), "application/vnd.android.package-archive");
context.startActivity(intent);
This is fine except a tiny but crutial detail:
the "path" string must start with file:// otherwise you'll get an exception such as
Unable to find an activity to handle the intent .....
So make sure the path starts with file://
Cheers.