If I’m not mistaken, all male ants have wings at some stage of their lives. So that on its own is not a very good clue for identification. I doubt anyone can give you a reliable ID without knowing where you are, either; a photo without a location is kind of meaningless. There are websites where you can post your pictures (like What’s That Bug), and someone will come to your rescue, but it may take some time. But it may not matter what species they are specifically.
I have often had ants invade my kitchen, and so have done quite a bit of reading in the past about getting rid of them. All ant poisons are based on a solution of borax in water with sugar, as @dxs suggests – though some use peanut butter instead of sugar and water; it depends on whether they’re likely to want solid or liquid food. Usually, the concentration of borax is about 5%, sometimes up to 8%. If you don’t want to mix it yourself (I never do), just buy bottle of it. If you hire an exterminator, they’ll probably do what you’ve already done: vacuum up the critters you can see, and then lay out a borax solution. They will likely look for a source – I imagine you can do that, too. Are they on the move? Coming from or going to anything in particular? Take a look and see if you can figure it out.
The borax poisons are meant not to kill the ants where they eat it. If they are dying where you lay it out, it’s too strong. They should be able to carry droplets of it back to the nest where it will kill the queen and destroy the colony.
But I’ll also add that ant outbreaks are often fleeting things. They will likely disappear on their own (or at least become invisible to you) shortly anyway. Personally, I prefer to fight them off, though. I’m kind of territorial that way.