The cockroaches entering my house seem to be flying more often than not. How do I get rid of them?
As a funny point of view: the way you ask, it is like: how to convince the cockroaches not to fly :)
Well, you need to find first the source of the insects (cockroaches or otherwise).
If they come through a window, use insect screens for those windows (ideally, for all windows).
If they come through special places (e.g. the "tunnel" hiding all the pipework, or the electrical conduits), then try to close the openings of those special places.
If there is an obvious place in your home which makes them flourish, get rid of their habitat.
Ideally, you track them thoroughly, until you find the main colony (if there is one) and get rid of the colony. Otherwise, in time, you may end up with an explosion of their number, when they find a new way in.
If you suspect that the situation is more serious, you may need to contact a company specialized in dealing with such situations.
We had, in our city, an ugly situation, when some ugly bugs were literally everywhere, inside and outside, covering everything, indoors and outdoors.
The owners of the houses / buildings and the management of the city repeatedly used chemicals, and tried new ones, until one of those chemicals was able to finish the nightmare.