I was given Duphaston 20mg daily for 14 days after my IUI. I got my periods 2 days late. Does this medication delay periods?

Yes. It can delay your period for a few days.
Duphaston and IUI. Duphaston is used to support the luteal phase of the menstrual cycle (the full cycle lasts on average 28 days) for in vitro fertilization. I am assuming that the attempt failed since you got a period. It is also used to treat heavy bleeding and irregular bleeding. I don't think the two are related except to indicate that the IUI did not take this cycle. Check with your OB to be sure.