Here's some code to get you started. As coded, the macro simply outputs the list of available fields to a message box.
Code:
Sub GetAllMergeFields()
Dim MMDF As MailMergeDataField, StrFlds As String
With ActiveDocument
If .MailMerge.MainDocumentType = wdNotAMergeDocument Then Exit Sub
For Each MMDF In .MailMerge.DataSource.DataFields
StrFlds = StrFlds & vbCr & MMDF.Name
Next
End With
MsgBox StrFlds
End Sub
To be able to select from the list, you'd need to output it to some kind of dropdown or listbox.