What happens if I have a Conspiracy / Arcane Adaptation then I cast one of the Flip-Walkers (Jace, Vryn’s Prodigy, Chandra, Fire of Kaladesh, Liliana, Heretical Healer, Nicol Bolas, The Ravager) My assumption is that without the self-exiling effect card flips to the walker side with no loyal counters and instantly kills itself. Please confirm?
The Planeswalker will have no loyalty counters and will die immediately from a state-based action.
This is stated in a Gatherer ruling on each of those cards. For example, the first five have this ruling:
In some rare cases, a spell or ability may cause one of these five cards to transform while it’s a creature (front face up) on the battlefield. If this happens, the resulting planeswalker won’t have any loyalty counters on it and will subsequently be put into its owner’s graveyard.
Transforming a card doesn't cause it to leave or enter the battlefield. It just turns into whatever is on its other face. So the planeswalker side doesn't "enter" with no loyalty counters, it just becomes the planeswalker side and doesn't have any loyalty counters.
If one of those cards enters the battlefield with its back face up for any reason, it enters the battlefield with a number of loyalty counters equal to its printed loyalty. Each of them has an ability that causes it to go to exile, and then enter the battlefield transformed, to ensure that it gets those loyalty counters.