What does the engine light mean when it is flashing and the car is running rough on a Mazda mille?

it is a warning that there is a major problem with your engine, and if you keep driving it, catasrophic engine damage can occur. it's in your owner's manual

Bottom Line -

FLASHING CEL, Park the car and TOW IT it the repair Place.
STEADY CEL, Drive it to any place that can pull the code and then decide.

not quite. we have 2 99's, and i have driven both with flashing cel. it helps to know what is going on, and not push it, but they can be driven. in one case, it was a fuel injector. easy change. another time, coils. actually, several times, coils. but you should drive it home, and then fix it.