How do I resize the chart to avoid legend overlap?

Is it possible to automatically resize the chart when the user changes the form size to prevent the legend from overlapping parts of the chart?

Below is an example of what is happening:

Initial form:

The user reduced the form size, and the legend overlapped part of the chart:

How can the chart be automatically scaled pie chart down to avoid this?

Yes. Enable automatic sizing for the pie and reserve space on the right for the legend:

with TMSFNCChart1 do
begin
  SeriesMargins.Right := 260;
  Series[0].Pie.AutoSize := True;
  Series[0].Legend.Position := lpCenterRight;
end;

SeriesMargins.Right prevents the pie from being drawn underneath the legend. With Pie.AutoSize enabled, the pie is automatically recalculated when the form or chart is resized.

Adjust 260 according to the width of your legend. No OnResize event is required.