Often a sign that the compost is too wet. You can get insecticide sticks which are pushed into the soil to deal with them Better if you keep the surface of the compost dryer. Try putting a good deep (1cm at least) layer of fine grit over the compost.

It's a common problem sadly. I agree with Owdboggy, keep the compost slightly drier so that the flies don't lay eggs and the larvae don't hatch, so breaking the life cycle of them.

You might have rotting meat in there. That will draw flies like the Dickens. Heap some earth on top. I wouldn't add meat to the compost pile, or meat products but that's a personal decision.

We routinely put a layer of grass mowings in the bin when the lawns are cut and rarely see flies. A shovelful of soil also works.

If it is compost in your compost bin [I thought you meant compost with a plant in it] then the fly larvae are breaking down some of the plant remains. Many flies in the compost are herbivorous rather than bluebottle types that lay eggs on rotting meat/animal wastes.

Personally I'd leave them alone.

There can be an annoyance though if the bin is quite near the house.(That's if the flies in question are the tiny fruit flies)

If it's the planting compost, Bacillus thuringiensis israelensis and/or beneficial nematodes are two different biological remedies that usually work.