Are you asking about the icon specifically, or just formatting in general?
I don't actually know whether you can in fact easily insert an image into
a RichTextBox; that is, I don't know of any specific methods on the
RichTextBox class (you can always edit the RTF directly, of course). Even
if you can, note that the example you gave for a blinking icon is not
inherent to the image; the ErrorProvider class starts a timer when you set
the error, and handles the blinking explicitly, outside the image data
itself. You would probably have to do something similar when trying to
cause an image in a RichTextBox to blink.
But as far as formatting in general goes, MSDN has a number of code
samples related to using the RichTextBox class, including examples of how
to set formatting using the various format-related properties and methods
on the class. As long as you are not dead-set on having a blinking image
in your RichTextBox, it should be reasonably straightforward for you to
implement what you want using the MSDN docs.