After back and forth emails with Xceed support. They were very kind to help me find the right solution for the problem.
Here is the code which works fine.
' Tell the browser we're sending a ZIP file!
Dim downloadFileName As String = String.Format("YourDownload-{0}.zip", DateTime.Now.ToString("yyyy-MM-dd-HH_mm_ss"))
Response.ContentType = "application/zip"
Response.AddHeader("Content-Disposition", "filename=" & downloadFileName)
Dim itemHeader As New ZipItemLocalHeader()
' Zip the contents of the selected files
Using zip As New ZipWriter(Response.OutputStream)
Dim directoryInfo As New DirectoryInfo(folderpath)
If directoryInfo.Exists Then
' Construct the contents of the README.txt file that will be included in this ZIP
Dim readMeMessage As String = String.Format("Your ZIP file {0} contains the following " & MainDirs.Length & " files:{1}{1}", downloadFileName, Environment.NewLine)
'Get files in the current directory and all subdirectories.
Dim _files As FileInfo() = directoryInfo.GetFiles("*.*", SearchOption.AllDirectories)
Dim buffer As Byte() = New Byte(65536) {}
Dim count As Integer = 0
For Each file As FileInfo In _files
'Create ZipItemLocalHeader for current item and write to archive.
Dim zipItemLocalHeader1 As New ZipItemLocalHeader(file.Name)
zip.WriteItemLocalHeader(zipItemLocalHeader1)
readMeMessage &= String.Concat(vbTab, (count + 1).ToString & "- ", Path.GetFileName(file.FullName), Environment.NewLine)
Using fs As FileStream = file.OpenRead()
'Write the current item's data to the zip archive
zip.WriteItemData(fs, buffer, 0, buffer.Length)
End Using
count += 1
Next file
itemHeader.FileName = "README.txt"
zip.WriteItemLocalHeader(itemHeader)
' Add the README.txt file to the ZIP
Dim data() As Byte = System.Text.Encoding.ASCII.GetBytes(readMeMessage)
zip.WriteItemData(data)
'Close the Zip archive. Writes the archive's central header.
zip.CloseZipFile()
End If
End Using