セルをダブルクリックすると編集モードになります。
このときセル内のテキストを全選択状態にするには、DoubleClickイベントまたはMouseDoubleClickイベントにて、非同期でSelectAllメソッドを実行し、エディタ上のすべての文字列を選択する方法が考えられます。



◎サンプルコード（VB）

Public Class Form1
    Private Sub Form1_Load(sender As Object, e As EventArgs) Handles MyBase.Load
        c1FlexGrid1.Rows.Count = 11
        c1FlexGrid1.Cols.Count = 5

        Dim i, j As Integer
        For i = 1 To c1FlexGrid1.Rows.Count - 1
            For j = 1 To c1FlexGrid1.Cols.Count - 1
                c1FlexGrid1(i, j) = i.ToString("00") + "_" + j.ToString("00")
            Next
        Next
    End Sub

    Private Sub c1FlexGrid1_DoubleClick(sender As Object, e As EventArgs) Handles c1FlexGrid1.DoubleClick
        If TypeOf c1FlexGrid1.Editor Is TextBox Then
            Dim editor = DirectCast(c1FlexGrid1.Editor, TextBox)
            editor.BeginInvoke(New MethodInvoker(Sub()
                                                     editor.SelectAll()
                                                 End Sub))
        End If
    End Sub

    Private Sub c1FlexGrid1_MouseDoubleClick(sender As Object, e As MouseEventArgs) Handles c1FlexGrid1.MouseDoubleClick
        'If TypeOf c1FlexGrid1.Editor Is TextBox Then
        '    Dim editor = DirectCast(c1FlexGrid1.Editor, TextBox)
        '    editor.BeginInvoke(New MethodInvoker(Sub()
        '                                             editor.SelectAll()
        '                                         End Sub))
        'End If
    End Sub
End Class

◎サンプルコード（C#）

namespace prj_C1FlexGrid
{
    public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();

            c1FlexGrid1.Rows.Count = 11;
            c1FlexGrid1.Cols.Count = 5;

            for (int i = 1; i < c1FlexGrid1.Rows.Count; i++)
            {
                for (int j = 1; j < c1FlexGrid1.Cols.Count; j++)
                {
                    c1FlexGrid1[i, j] = i.ToString("00") + "_" + j.ToString("00");
                }
            }
        }

        private void c1FlexGrid1_DoubleClick(object sender, EventArgs e)
        {
            if (c1FlexGrid1.Editor.GetType().Name == "GridEditorTextBox")
            {
                TextBox editor = (TextBox)c1FlexGrid1.Editor;
                editor.BeginInvoke(new MethodInvoker(() =>
                {
                    editor.SelectAll();
                }));
            }
        }

        private void c1FlexGrid1_MouseDoubleClick(object sender, MouseEventArgs e)
        {
            //if (c1FlexGrid1.Editor.GetType().Name == "GridEditorTextBox")
            //{
            //    TextBox editor = (TextBox)c1FlexGrid1.Editor;
            //    editor.BeginInvoke(new MethodInvoker(() =>
            //    {
            //        editor.SelectAll();
            //    }));
            //}
        }
    }
}