The Prophet of Kruphix has the ability
You may cast creature cards as if they had flash.
Does this apply to the Loyalty ability
Put three 1/1 white soldier creature tokens onto the battlefield
of the Planeswalker Elspeth, Sun's Champion?
No, there's no overlap here at all, for two reasons.
Casting a creature card is the process you go through to put Prophet of Kruphix on the battlefield in the first place:
That's the casting part. Hopefully, it doesn't get countered. When the spell resolves, the creature lands on the battlefield.
Sometimes it's a little different: a card with Flashback (Ancient Grudge) can be cast from your graveyard rather than your hand. A card with Cipher (Paranoid Delusions) has a free copy cast of it sometimes. But the process is still the same: the creature, or the spell, goes on the stack.
Elspeth's ability isn't the same thing. It's a loyalty ability and it's that ability that goes on the stack. When it resolves, it puts some creature tokens on the battlefield. The ability is used, but a spell isn't cast. Also, the tokens may get represented by physical cards, but they're still tokens and don't count as cards.