Try outputting the record *before* you move to the next input record.
Code:
Private Sub cmdExportDB_Click()
Dim rst As DAO.Recordset
Dim db As DAO.Database
Dim fld As DAO.Field
Dim strText As String
Dim track1 As String
Dim track2 As String
Dim track3 As String
Dim badge As String
Set db = CurrentDb
track1 = Chr(1)
track2 = Chr(2)
track3 = Chr(3)
Set rst = db.OpenRecordset("select * from export")
Open "c:\badges\here.txt" For Output As #1
Do While Not rst.EOF
For Each fld In rst.Fields
badge = track1 & vbNewLine & track2 & fld.Value
strText = badge & vbNewLine & track3 & vbNewLine & vbNewLine
Next
Print #1, strText
rst.MoveNext
Loop
Close #1
rst.Close
Set rst = Nothing
End Sub