If you happen to ingest or swallow fly eggs or flies and they lay eggs in your stomach then fly eggs should not have time to hatch the fly eggs in your stomach.
When you swallow flies or fly eggs the stomach acid should digest the flies and fly eggs and kill them before they have time to hatch.
So as long as your stomach acid digests and kills the fly eggs or flies that you swallowed then no they cannot hatch in your stomach.
If you do happen to ingest or swallow a fly or fly eggs then there's no need to worry and you should not get sick.
The stomach acid should easily digest the fly or fly eggs and then you poop the rest of it out eventually.