There's a setting under Speech, Inking, and Typing. To get there, 
1. First, go to Settings and click "Time & Language". 
2. Select the "Speech" option.
3. Go to the "Speech, Inking & Typing privacy settings".
4. Then, click on the pop-up and turn the setting ON.
After that, any software that uses the Speech Recognition API will work.
A helpful way to tell users to turn on would be...
catch (System.Runtime.InteropServices.COMException e) when (e.HResult == unchecked((int)0x80045509))
//privacyPolicyHResult
//The speech privacy policy was not accepted prior to attempting a speech recognition.
{
    ContentDialog Dialog = new ContentDialog()
    {
        Title = "The speech privacy policy was not accepted",
        Content = "You need to turn on a button called 'Get to know me'...",
        PrimaryButtonText = "Shut up",
        SecondaryButtonText = "Shut up and show me the setting"
    };
    if (await Dialog.ShowAsync() == ContentDialogResult.Secondary)
    {
        const string uriToLaunch = "ms-settings:privacy-speechtyping";
        
        //"was-not-accepted-prior-to-attempting-a-spee/43083877#43083877";
        var uri = new Uri(uriToLaunch);
        var success = await Windows.System.Launcher.LaunchUriAsync(uri);
        if (!success) await new ContentDialog
        {
            Title = "Oops! Something went wrong...",
            Content = "The settings app could not be opened.",
            PrimaryButtonText = "Shut your mouth up!"
        }.ShowAsync();
    }
}