WrapperStream.cs

class WrapperStream : Stream
{
    readonly HttpResponseMessage _httpResponseMessage;
    readonly Stream _stream;
    public WrapperStream(HttpResponseMessage httpResponseMessage, Stream stream)
    {
        this._httpResponseMessage = httpResponseMessage;
        this._stream = stream;
    }
    public override bool CanRead => _stream.CanRead;
    public override bool CanSeek => _stream.CanSeek;
    public override bool CanWrite => _stream.CanWrite;
    public override long Length => _stream.Length;
    public override long Position { get => _stream.Position; set => _stream.Position = value; }
    public override void Flush() => throw new NotImplementedException();
    public override long Seek(long offset, SeekOrigin origin) => throw new NotImplementedException();
    public override void SetLength(long value) => throw new NotImplementedException();
    public override void Write(byte[] buffer, int offset, int count) => throw new NotImplementedException();
    public override int Read(byte[] buffer, int offset, int count)
        => _stream.Read(buffer, offset, count);
    public override IAsyncResult BeginRead(byte[] buffer, int offset, int count, AsyncCallback callback, object state)
        => _stream.BeginRead(buffer, offset, count, callback, state);
    public override IAsyncResult BeginWrite(byte[] buffer, int offset, int count, AsyncCallback callback, object state)
        => _stream.BeginWrite(buffer, offset, count, callback, state);
    protected override void Dispose(bool disposing)
    {
        _stream.Dispose();
        _httpResponseMessage.Dispose();
        base.Dispose(disposing);
    }

    static HttpClient _client = new HttpClient();
    public static async void Test()
    {
        using HttpRequestMessage httpRequestMessage = new HttpRequestMessage(HttpMethod.Get, "https://videoabc.com");
        HttpResponseMessage httpResponseMessage = await _client.SendAsync(httpRequestMessage,HttpCompletionOption.ResponseHeadersRead);
        if(httpResponseMessage.IsSuccessStatusCode)
        {
            Stream stream = await httpResponseMessage.Content.ReadAsStreamAsync();
            Response.OutputStream = new WrapperStream(httpResponseMessage, stream);
        }
        else
        {
            //báo lỗi
        }
    }
}