Hi Fakharsherazi. Welcome to NGA!
Diluted hydrogen peroxide will kill some things, maybe larvae?
Try 0.2% H2O2. Drench the soil often enough to kill the hatching maggots.
If you can buy "drugstore peroxide", it will be around 3% strength, so you would dilute that by 16:1. For example,
2 ounces 3% H2O2 + 1 quart water.
But, if the soil is very fine, it will hold a lot of water and not drain very well. "Compost plus peat" sounds VERY finely divided and very water-retentive, and NOT well aerated or fast-draining. If you get them past all the hatching living things, the seedlings will still have to survive "damping off" as they grow through the organic-rich, microbe-rich soil. And that rotting compost will attract lots of fungus and flies.
I agree that, IF you use compost to start seeds, it should be very well-finished compost, to reduce the number of microorganisms and insect eggs by as much as possible.
If you do use FINISHED compost , add something to the seedling mix that promotes aeration and fast drainage - something coarse, like crushed stone or grit, Perlite, or pine bark shreds.
Starting seedlings in a near-sterile soilless mix might be wiser than using compost plus other fine particles.
BTW, I thought the main value of chicken manure was all the nutrients, especially nitrogen, that it contributes. But seedlings need very LOW nutrient levels!