Until the find all flights of a given airline function is available, I’ve found a workaround to locate the flights. I use google to locate the flights. My results show that many, but not all, of the flights for a given operator are shown. Remember, this is just a workaround and is not by any means perfect. One of the shortcomings is that is appears to look at the top blue line of the FlightAware screen to get the data. So, while you could enter N690E, for example, and locate the flight, it won’t locate the operator of the aircraft (“Teufel Lawrence (Portland, OR)”).
Here’s some examples. The number at the end indicates the number of hits. Take this number with a grain of salt because quite often google shows only the most relevant results and omitts entires that are similar to the ones already shown, although it does allow for the search to be repated wth the omitted results shown.
“southwest” site:flightaware.com 741
"horizon airlines" site:flightaware.com 115
"american airlines" site:flightaware.com