Private m_DBConnection As ADODB.Connection
' Connect to the database.
Private Sub cmdConnect_Click()
    ' If a database is currently open, close it.
    If Not m_DBConnection Is Nothing Then
        If m_DBConnection.State <> adStateClosed Then _
            m_DBConnection.Close
    End If

    Set m_DBConnection = New ADODB.Connection
    m_DBConnection.ConnectionString = _
        "Provider=Microsoft.Jet.OLEDB.4.0;" & _
        "Data Source=" & txtDatabase.Text & ";" & _
        "Persist Security Info=False"
    m_DBConnection.Open

    cmdExecute.Enabled = True
End Sub

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 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

    ' Open the Recordset.
    Set rs = m_DBConnection.Execute( _
        txtCommand.Text, , 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

    Set frmIcons.Font = flxGrid.Font
    new_wid = frmIcons.TextWidth(rs.Fields(c).Value)

Thanks Gary.