Is it possible to programmatically uninstall a package in Android

A 3rd party app cannot install or uninstall any other packages programmatically, that would be a security risk for Android. However a 3rd party app can ask the Android OS to install or uninstall a package using intents, this question should provide more complete information:

install / uninstall APKs programmatically (PackageManager vs Intents)

In Kotlin, using API 14+, you can just call the following:

startActivity(Intent(Intent.ACTION_UNINSTALL_PACKAGE).apply {
     data = Uri.parse("package:$packageName")
})

Or with Android KTX:

startActivity(Intent(Intent.ACTION_UNINSTALL_PACKAGE).apply {
     data = "package:$packageName".toUri()
})

It will show the uninstall prompt for your app. You can change packageName to any package name of another app if needed.