You can check current default launcher by this piece of code:
Intent intent = new Intent(Intent.ACTION_MAIN);
intent.addCategory(Intent.CATEGORY_HOME);
ResolveInfo resolveInfo = getPackageManager().resolveActivity(intent, PackageManager.MATCH_DEFAULT_ONLY);
String currentHomePackage = resolveInfo.activityInfo.packageName;
as shown in this answer: How can I get the package name of the current launcher in android 2.3 and above?
So simply check if currentHomePackage
equals your App's Package and act accordingly.
If the user sets another App as Default Launcher the Dialog to choose a Default Launcher would only appear again if he delets the Launchers Defaults or removes/installs an App which can act as default launcher.