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Hi Harry, 

They can in theory, but total solar eclipses last only a few minutes, so the chance of a flare occuring on the limb of the Sun during that time is not so big. Maybe someone has seen one, though. It has been suggested that a 1800s  drawing of a total eclipse (see below) shows a coronal Mass Ejection (CME). Those would be easier to see during an eclipse - they are much larger in extent than flares - but you would still need to be lucky.

Total solar eclipse drawings thought to show a CME: http://sunearthday.nasa.gov/2006/locations/firstcme.php 

Terry 

Sometimes people call the red extensions at the edge of the eclipsed sun (peeking out from behind the moon) as "flares" but they are really just prominences, material flung out from the Sun. The prominences are red because they contain a lot of Hydrogen. You can see some great eclipse pictures from the China eclipse that has prominences near the "3 o'clock" position at: http://www.eclipsetours.com/cresults.html You can see prominences any day using a Hydrogen-alpha filter. You can see today's h-alpha image by going to http://sunearth.gsfc.nasa.gov/spaceweather/ and choosing "H-Alpha Full Disk ... from Kanelhohe" but if the Sun is really quiet, like now, you won't see many prominences.