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?
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.