There is a shuttle between the end of the Green Line and the Metrolink station, although I haven't taken it myself.
I agree that arriving in Santa Ana 1:15 before the flight leaves from the SNA airport is cutting it close. That's the first outbound train of the day. Trains to BUR run more frequently.
Just curious, why did you book an itinerary like this? Leaving SNA just a little later would work out nicely via the train.