How about this: Flurry Heart was born as an alicorn because Cadance was already pregnant with her when Lord Tirek attacked, and as a result was exposed to the rainbow power of Harmony, causing her to be what she is.

Then when the pregnancy was revealed it should have been visible, because Tirek’s attack happened a while back.

Although canon time in the show seems to be hard to guess based on anyone’s guess at times.

But I think that’s too far back even if it would be a time where the egg had JUST been fertilized, to excuse Flurry Heart’s alicornhood on the whole the Rainbow Power thing set loose.