The Check light flashes everytime you start the car until you press the brake pedal, and will continue to flash if one of the other lights on the check panel is on.
If you press the button on the check panel, the flashing light will extinguish and just leave the coolant light on.
The coolant light may be a faulty sensor (they corrode), so if your coolant is OK, either buy a new sensor (recommended for peace of mind), or short the two wires from the sensor together. You can actually do this by pulling the sensor apart and shorting the two electrodes inside the sensor - that way if you ever buy a new sensor you havn't cut any wires.
Resetting Service Indicator Lights