The flashing would be in the generator start switch, but I doubt if your '89 LaSalle has a genset with electronic self-diagnostics that would produce the flashes that John described.
There are two possibilities for the problem you describe:
1. The a/c compressor is drawing far to many amps. Can you hook up to shore power briefly to see if it also trips the breaker on that source?
2. The genset voltage regular & speed governor are working and the genset does not respond when the power load increases. When the compressor kicks in and the amps jump dramatically, the genset must respond quickly by opening the throttle to keep the RPMs up. If it doesn't, it will either die or a breaker trips because the voltage drops and the amps go up.
You can get a better idea about the genset governor by using a different heavy load, e.g. an electric space heater. If the genset or breaker goes out with that, the problem is more likely the genset than the a/c unit.