Flies do die after laying eggs but it's not because they lay eggs.
Flies including houseflies have a lifespan of 28 days to 31 days after they hatch and live so a flies lifespan is very short.
Even when you don't kill the flies around you the flies are gonna die soon anyway.
Although flies lay eggs that turn into maggots which then turn into adult flies and the flies replicate pretty quick.
If flies land in your food it's better to throw the food out because they may have laid a fly egg or eggs into the food which then turn into maggots.
But if a fly flew into your drink and you removed it right away then it should be no issue.
I have had flies land in my tea and sometimes cup of coffee and I just remove the fly and continue to drink my tea and coffee.
But if flies landed in my food then I would throw it out.
They may have laid eggs in the food that you cannot see.