Can a planeswalker's loyalty ability be activated at instant speed if granted flash?

Flash (CR 702.8) is a keyword that allows a spell to be cast at any time you could cast an instant. It has no effect on the activation of abilities, including loyalty abilities. These are two fundamentally different actions in the rules — casting a spell versus activating an ability.

Loyalty abilities are governed by CR 606.3, which states they may only be activated at sorcery speed: specifically, only during your own main phase, when the stack is empty, and only if the planeswalker has been under your control since the beginning of your current turn (the 'summoning sickness' analog for planeswalkers, CR 306.5). No rule exists that would let flash override these restrictions.

Even if a planeswalker card somehow had the flash keyword printed on it (affecting how it's cast), that keyword would grant no special timing permission to its loyalty abilities once the permanent is on the battlefield. The permanent's abilities are not spells.

Concrete example: Suppose Teferi, Master of Time is on the battlefield. His loyalty abilities still can only be activated during your main phase with the stack empty, even if you somehow granted the card flash. Flash would only matter if you were casting Teferi from your hand.

In summary, granting flash to a planeswalker — whether via a card effect or a hypothetical rules scenario — does not grant its loyalty abilities instant speed. Only a specific rule or card effect that explicitly allows activating loyalty abilities at instant speed (none currently exist in this form) could change this.