The general rule of thumb with a Check Engine Light (CEL) is that a steadily illuminated light means that the OBD II system should be scanned and car should be checked as soon as it is convenient. In other words, not an emergency, but something that bears checking.
However, when a CEL begins to blink on and off, this is supposed to indicate an situation that needs to be investigated immediatedly before one problem morphs into more than one, and before repair costs escalate.
As to a CEL that blinks upon starting the engine and then shuts down for the duration of the drive, I have to say that I don't know the specific answer, but I have two suggestions:
*Read what your Owner's Manual may have to say on the topic. It is possible that there may be an explanation for this CEL behavior.
*Have the OBD II system scanned a.s.a.p. at an auto parts retailer who does this free-of-charge. You can try Auto Zone, Advance Auto Parts, and O'Reilly as possible sources of this free service.
Just in case this CEL pattern does indicate something serious, I would suggest having the scan done tomorrow. Even if there is no serious problem, in most cases cars use more gas and emit more pollutants whenever a CEL is lit up, so you can potentially save a bit of money by doing this sooner, rather than later.