I remember the first time I saw a cockroach in my apartment I was terrified of it and of being called an untidy person. After a short time that fear faded and every time I saw one I immediately went on the war path.
Kill the roach, find where it came from, patch the hole, vacuum the area, wash the area, spray the area, triple check there's no food or dampness for them to live on. It was work but my unit had far fewer cockroachs than many other units.
Some Australian cockroaches definitely fly but don’t seem to do it very often. They’re quite noisy when they fly—kind of like the propeller sound you make if you trill your tongue—and there’s nothing worse than hearing that sound suddenly stop very close to you. ‘Oh fuck! Have I got a cockroach on me?’ I hate them.
Hawaii has big ones. When I lived there, going to the kitchen at night and opening the fridge or turning on the light almost always had at least one flying towards your face. That's the only time I've seen them fly. Guessing they can't fly far, but are capable as a quick escape mechanism.