I have cherry tomatoes a few burst in the plastic box,& there are flies. Should I throw them all out, or can I keep the firm ones and wash them well?

Keep and wash the firm ones, but use up quickly. There may still be fly eggs on there waiting to hatch. Might be a good opportunity to freeze the tomatoes for later, then get them out as you need them for sauces and such.

Question: what kind of flies are they? Fruit flies or house flies?

Keep and wash!