Use the recordset's Fields collection to get the field names and values. Keep track of the width of the text in each column and size the grid's columns accordingly.

Private Sub cmdExecute_Click()
Dim query As String
Dim i As Integer
Dim db_name As String
Dim connect_string As String
Dim rs As ADODB.Recordset
Dim r As Integer
Dim c As Integer
Dim num_cols As Integer
Dim col_wid() As Single
Dim new_wid As Single

    ' Get the list of fields selected.
    For i = 0 To lstFields.ListCount - 1
        If lstFields.Selected(i) Then
            query = query & lstFields.List(i) & ", "
        End If
    Next i

    ' Remove the final comma.
    query = Left$(query, Len(query) - 2)

    ' Build the query.
    query = "SELECT " & query & " FROM Books"

    ' Get the database name.
    db_name = App.Path
    If Right$(db_name, 1) <> "\" Then db_name = db_name & _
        "\"
    db_name = db_name & "books.mdb"

    ' Build the connect string.
    connect_string = _
        "Provider=Microsoft.Jet.OLEDB.4.0;" & _
        "Data Source=" & db_name & ";" & _
        "Persist Security Info=False"

    ' Open the recordset.
    Set rs = New ADODB.Recordset
    rs.Open query, connect_string, _
        adOpenForwardOnly, adLockReadOnly, _
        adCmdText

    ' Hide the grid.
    flxResults.Visible = False
    DoEvents

    ' Display the results.
    If rs.EOF Then
        flxResults.Rows = 1
        flxResults.Cols = 1
        flxResults.TextMatrix(0, 0) = "No Records Selected"
        num_cols = 1
        ReDim col_wid(0 To 0)
        col_wid(0) = TextWidth(flxResults.TextMatrix(0, 0))
    Else
        ' Make room for column widths.
        num_cols = rs.Fields.Count
        ReDim col_wid(0 To num_cols - 1)

        ' Set column headers.
        flxResults.Rows = 2
        flxResults.Cols = num_cols
        flxResults.FixedCols = 0
        flxResults.FixedRows = 1
        For c = 0 To num_cols - 1
            flxResults.TextMatrix(0, c) = rs.Fields(c).Name

            ' See if we need to enlarge the column.
            new_wid = TextWidth(rs.Fields(c).Name)
            If col_wid(c) < new_wid Then col_wid(c) = _
                new_wid
        Next c

        ' Display the data.
        Do Until rs.EOF
            r = r + 1
            flxResults.Rows = r + 1
            For c = 0 To rs.Fields.Count - 1
                flxResults.TextMatrix(r, c) = _
                    rs.Fields(c).Value

                ' See if we need to enlarge the column.
                new_wid = TextWidth(rs.Fields(c).Value)
                If col_wid(c) < new_wid Then col_wid(c) = _
                    new_wid
            Next c
            rs.MoveNext
        Loop
    End If

    ' Set the grid's column widths.
    For c = 0 To num_cols - 1
        flxResults.ColWidth(c) = col_wid(c) + 120
    Next

    ' Display the grid.
    flxResults.Visible = True

    rs.Close
End Sub