In the past the check engine light on my 97 Civic SI would come on when there was a misfire during starting.
The light would either go out on it's own some time later or was reset by my mechanic.

At this time the car has begun intermittent misfiring while running and the light flashes on and off when this occurs. The light stops flashing but remains on for some time after the misfiring subsides.

When misfiring there is a distinct lack of power so I assume it's only firing on 3 cylinders.

Should I check the plugs or is this more likely to be an expensive control module?

RSVP

How old are the plug wires? They don't last forever... and when was the distributor cap and rotor replaced AND the plugs?

The flashing CEL means you need to take immediate action; otherwise you could damage the engine and/or catalytic converter. I would:

. Replace spark plugs (NGK only), if they have been in more than 3 years.

. Replace plug wires, if they have not been changed in 80,000 miles.

. Replace Ignition Control Module (ICM) and coil, if they have not been changed in 120,000 miles or 10 years, whichever comes first.

. Check for a vacuum leak, especially with the intake manifold gasket. Use a spray bottle of water with the engine running.