The CEL flashes when there's a problem with the engine that is considered "serious" and can harm the engine or emissions system. The cruise control is automatically disabled when the CEL is on, thus the flashing cruise light.
No telling what causes the CEL without reading the trouble code or codes that would stored in the engine control module's memory, but it could be something like a cylinder misfire.
On some years it's possible to read the codes from the instrument panel; others require an OBD code reader. Perhaps indicate information about the car (year, model, engine, transmission, mileage, recent work done, major service schedule items completed, and where you are, and we'll try to fill in more details.