The good news is that there *IS* an effective way to get rid of fire ants.
Per the experts at Texas A&M, the best way to get rid of fire ants is to use Fipronil (trade names: Top Choice, Taurus G, Quali-Pro). It's a once a year application.
We have used it in our small neighborhood west of Austin, where we had a horrid fire ant infestation that was making using our yards pretty much impossible. We got everyone to agree to have it applied to their yards at the same time, as well as applying it to the neighborhood common areas. A few weeks after the first treatment, the ants were gone enough that kids could play in the yards without getting chewed. After a couple of years, we have completely eradicated the fire ants from everyone's yards, and now we just treat every other year. (It's what is used on playgrounds, parks, commercial properties, etc.)
Now the bad news.
This stuff is a restricted use product, available to licensed applicators only — unless you have an exterminator's license, you can't go buy it and do it yourself. And it's not cheap — to treat an acre, you need about 87 pounds of product, which is about $100 (plus paying the applicator to spread it). If you go in with your neighbors and split the cost, it can reduce the price and improve the efficiency, but it's not gonna be like buying a jug of Amdro.
You also don't want to use it in your veg gardens (I use spinosad bait there, and treat the rest of the yard with Fipronil).