Peat moss is what is usually used to incubate killifish eggs. The incubation time varies with different species but the eggs of the Nothobranchius will hatch in 6 to 8 weeks. The peat should always be stored in a dark,cool place. A styrofoam box is best because it will keep the temperature constant. "Eyed-up" eggs, which just means when you look at the eggs you can see little fishy eyes, mean the eggs are fully developed. When "eyes" appear in the eggs, it's "Hatching time".
When you are ready to hatch the eggs, keep them in the peat when you wet them. The eggs won't hatch without the peat.
Wet the peat with aged water to a depth of about 5 cm. It's best to use water from an established fish tank.
If the timing is right, you should see fry within a few hours. If not, wait at least 2 days.
I've never hatched Killiefish, just getting this from what I've read and a few clients who did over the years. I Did hatch cuttlefish at one time though...