In effetti per VB.BET non c'è molto sul web...

Eccoti le dichiarazioni per VB.NET con i flag più utilizzati:

codice:
    ' -----------------------------------------
    ' SHFileOperation in VB.NET
    Private Structure SHFILEOPSTRUCT
        Dim hwnd As Integer
        Dim wFunc As Integer
        Dim pFrom As String
        Dim pTo As String
        Dim fFlags As Short
        Dim fAnyOperationsAborted As Boolean
        Dim hNameMappings As Integer
        Dim lpszProgressTitle As String
    End Structure

    Private Declare Function SHFileOperation Lib "shell32.dll" Alias "SHFileOperation" (ByRef lpFileOp As SHFILEOPSTRUCT) As Integer

    Private Const FOF_ALLOWUNDO As Short = &H40
    Private Const FOF_CONFIRMMOUSE As Short = &H2
    Private Const FOF_NOCONFIRMATION As Short = &H10S
    Private Const FO_COPY As Int32 = &H2
    Private Const FO_DELETE As Int32 = &H3
    Private Const FO_MOVE As Int32 = &H1
    Private Const FO_RENAME As Int32= &H4
    Private Const FOF_SILENT As Int32 = &H4
    Private Const FOF_RENAMEONCOLLISION As Int32= &H8
    Private Const FOF_SIMPLEPROGRESS As Int32= &H100

Tieni presente che questa funzione di sistema (quella che mostra il dialogo standard) e 'ricrea' la struttura delle cartelle, nel tuo caso andrà chiamata per ogni file del tuo FilesListBox.
Il link con la documentazione te l'ho già postato, non ti resta che procedere.