That’s certainly not true. You cannot foresee the implications of all flies (i.e. the order Diptera) to go extinct. There are many that are pollinators and others (including mosquitoes (Culicidae)) that are important food source for other animals. Without flies the food web would change a lot and we don’t know what effect it would have on humans. But pretty sure that the ecosystem would be even less resilient and be more endangered to collapse.