This is really out of scope of the article but here is a quick review:

Well it looks like you don’t need a singleton with argument at all, since you want to create a new AppAPI instance every time the config changes. Also, your ApiController2 class probably leaks an activity because it keeps a reference to Context.

You can still make the OkHttpClient a singleton. In your example, since it doesn’t need any Context to be built, you can simply use a property inside an object. Here’s the idea:

object ApiFactory {
    private val okHttpClient = OkHttpClient.Builder()
            .dispatcher(Dispatcher())
            .connectionPool(ConnectionPool())
            .build()

    fun buildAPI(context: Context): AppAPI {
        val baseUrl = loadBaseUrlFromConfig(context)

        return Retrofit.Builder()
                .addConverterFactory(GsonConverterFactory.create())
                .client(okHttpClient)
                .baseUrl(baseUrl)
                .build()
                .create(AppAPI::class.java)
    }
}

Then once you build the AppAPI object you should keep it around in a var somewhere in order to not rebuild it for each HTTP request. But it’s definitely not a singleton since you may have to replace it with a different instance later.