If  you have an infinite Transfer-Encoding: Chunked HTTP response, you can read it this way:

private async void Foo()
{
    // Example URI.
    Uri uri = new Uri("http://localhost/?chunked=1&length=10000000000&delay=500");

    HttpClient client = new HttpClient();
    HttpResponseMessage response = await client.GetAsync(
        uri,
        HttpCompletionOption.ResponseHeadersRead);
    IInputStream inputStream = await response.Content.ReadAsInputStreamAsync();

    ulong totalBytesRead = 0;
    IBuffer buffer = new Windows.Storage.Streams.Buffer(1000000);
    do
    {
        buffer = await inputStream.ReadAsync(
            buffer,
            buffer.Capacity,
            InputStreamOptions.Partial);

        // ...

        totalBytesRead += buffer.Length;
        Debug.WriteLine(buffer.Length + " " + totalBytesRead);
    } while (buffer.Length > 0);

    Debug.WriteLine(totalBytesRead);
}