Not using the Zip implementation, but I had a similar problem trying to use CreateWorkbookExporter to export directly to the Response.OutputStream.  To make this work I created a seek-ignoring stream class that fakes the necessary methods:

        public class SeekIgnoringStream : Stream
        {
            private readonly Stream _outputStream;
            private bool _seekPerformed = false;

            public override bool CanRead => _outputStream.CanRead;

            public override bool CanSeek => true;

            public override bool CanWrite => true;

            public override long Length => _outputStream.Length;

            public override long Position { get => pos; set { } }

            public SeekIgnoringStream(Stream outputStream)
            {
                _outputStream = outputStream;
            }
            long pos = 0;
            public override void Write(byte[] buffer, int offset, int count)
            {
                _outputStream.Write(buffer, offset, count);
                pos += count;
                _outputStream.Flush();
            }

            public override void Flush()
            {
                _outputStream.Flush();
            }

            public override long Seek(long offset, SeekOrigin origin)
            {
                // Ignore the initial seek
                if (!_seekPerformed)
                {
                    _seekPerformed = true;
                    return 0;
                }

                // Otherwise, delegate to the output stream
                return _outputStream.Seek(offset, origin);
            }

            public override void SetLength(long value)
            {
                //_outputStream.SetLength(value);
            }

            public override int Read(byte[] buffer, int offset, int count)
            {
                return _outputStream.Read(buffer, offset, count);
            }
        }

And then to use it you wrap the non-seekable stream in a SeekIgnoringStream like so:

            using (var ms = new SeekIgnoringStream(Response.OutputStream))
            {
                using (IWorkbookExporter workbook = SpreadExporter.CreateWorkbookExporter(SpreadDocumentFormat.Xlsx, ms))

                { ...

At least for a basic implementation writing a single worksheet to Response.OutputStream this does work as basically an unbuffered write operation to the browser.  Note that you do need to set Response.BufferOutput = false before this or else it will still buffer in memory.  I haven't looked at the Telerik internals for this, so I'm not sure under what conditions this might break.