Because of their life cycle it is all but impossible to raise syrphids comercially. They lay their eggs singly on plant stalks where there are aphids. The maggot hatches out and begins hunting up and down plant stalks for aphids to eat. It them pupates and hatches into a fly.
The adults feed on nectar and your best bet is to make sure they have plenty of the blossoms they prefer. Number one on their hit list is Queen Annes lace. They also like perennial (but not annual) marigolds such as tagetes lucida and Copper Canyon daisies. If some of your carrots flower don't pull them out. Those flowers are also favored. I've seen yarrow listed as a good forage plant but the ones in my garden don't seem to care for it. Fortunately the flowers preferred by syrphids are also favorites with the tiny parasitic wasps which hunt aphids and whitefly.

They exist in your garden /landscape already. Favor them & they will multiply.

Good advice. Yes, they exist in quite large numbers anywhere gardens can be grown and can fly long distances to find favorable conditions. Try to make sure those favorable conditions are in your garden. Many of our beneficial insects go about their work so quietly we don't even notice them if we aren't looking for them.

One of the things that attracts syrphid flies is a large, succulent crop of tender aphids.

When aphids first appear, they have few predators and they multiply rapidly - that's the point that most gardeners panic and break out the insecticide ... and the adults never show up.

What I do is DO NOTHING and the predators show up and everything gets back into balance.

Daisy-like flowers for the adult pollen and nectar-eating adults is good, but if there are no aphids for baby food, they won't bother laying eggs.

Here is a link that might be useful: Natural Pest control

Thanks for the answers. I wasn't aware it was impossible to raise them commercially. I do have some visiting my yard but I was hoping to augment their population at least for the rest of this summer. I don't know what's up this year here - very few bumble bees, lady bugs or other beneficials. On the plus side, I saw some parasitic wasps.