The SES light flashing is telling you that there are multiple missfires, its really weird that you're not getting a code...

Since you've already checked your electrical system, start looking into your fuel system. Since it sounds like you have had this problem since you got the car, I would start at the tank and see if you see any impurities in a sample from it. Then check your fuel filter to make sure its not clogged. Then check your injectors and run some injector cleaner or seafoam in the tank.

If you do all that and it doesn't check out, it could be an issue with the crank position sensor, or tune. I say tune because if no codes are coming up, they could have been set to not report.