Sort of. Flies don't necessarily carry more diseases than other insects, if fact they carry far fewer than many, such as mosquitoes, but they are much better at transmitting them than most.
Flies eat by vomiting on food, which dissolves it outside their bodies so that they can suck it up like a straw. Because of this, they leave residues on whatever food they land on. So if the fly is carrying a disease, it could be on there too.
For comparison's sake, roaches are actually relatively clean. They have mouths and are highly unlikely to leave anything harmful behind if they get into your food. Like most insects, they usually contaminate food only if they walk through something harmful, then walk through something that you would consume.
Flies are also much more common than other types of insects that are actually better at passing on disease. Mosquitoes need standing water in order to reproduce and are rarely found in arid climates. Tics are found mainly in wooded areas, which is not where most people live. Flies can be found practically anywhere.
As far as kitchens are concerned, forget the roaches and spiders. Flies should be your biggest priority.