There are flying ants already - they're called wasps (actually it's the other way around, ants are wingless wasps).
Argentines may be an issue but they need it really moist and can only survive with a constant water supply (that's why they mostly nest near humans settlements and rivers). Pheidole megacephala (big headed ants), another invasive supercolony ant species which is even worse than Argentines, usually just shreds through them. I'm also pretty curious how things will work out when Argentines and Nylanderia fulva (Raspberry crazy ants, resistant to fire ant stings and currently butchering their way through Florida) will meet. Not to forget yellow crazy ants which are currently devastating dozens of pacific islands. And i'm pretty sure it's just a matter of time until we have to deal with some sort of invasive Crematogaster acrobat ants as well (apparently there actually is a Crematogaster species currently invading Crimea).
There's a good amount of invasive species by now (also worth mentioning the super tiny Tapinoma melanocephalum Ghost ants and the ominous Lasius neglectus that is the only temperate ant capable of founding supercolonies) and Argentines really aren't the worst in general - yellow crazy ants for example are way more devastating to their environemnt. It all depends on how adaptive a species is and what environment a specific location offers them, every place is different and allows a different invasive species to thrive most.