Is it possible to flash out of the way of a spell that occurs almost instantly?

In League of Legends there are 3 major type of spells. Targeted, Self-Cast and Skillshots.

Targeted abilities are locked on the target. If the target moves or flashes away, the ability will still hit the target (Like Annie's Q or Ranged Basic Attacks)

Self Cast or Stance abilities only work on yourself, you cannot target them on a teammate (but it can still benefit teammates, such as Sona's Basic Abilities)

Skillshots are aimable by the caster, but their travel path is constant. If one is coming your way you can flash or just dodge it. Blitzcrank's grab is a skillshot, so you can dodge it.

However, you cannot flash away from the hook once it lands on you, similarly to Darius' E. There is an exception to this - Ezreal's E (a blink/dash) is able to prevent being pulled, while visually making Blitzcrank's arm extend even further (which is so funny)

The answer is Yes

You can flash a blitz hook easily. You just have to time it correctly.

You can even dodge an Ezreals Ultimate by flashing (even towards him). Many players do this. They are in a tight skirmish and they see an opportunity to be agressive or re-engage and flash the skillshot to do so and finish off an opponent.

It's all about timing and reactions.

A number of skills can be flashed from to dodge them. Any skill shot can be flashed away from to dodge it with proper timing. Most other skills (targeted ones) cannot be flashed away from, as they will follow you (i.e. Caitlyn ultimate, Malphite seismic shard, etc) but certain skills can with proper timing (i.e. Alistar headbutt, and select others). However there can be good reason for flashing from targeted abilities, as if cait ults you, you can flash behind a team mate and the ult will hit them instead, provided they stand in the path the ult is traveling. Also flashing behind a yasuo wall or braum unbreakable shield will cause any particle from a targeted ability to be destroyed one the wall. However since while flashing, until the animation completes, you are considered to still be in the place you are flashing from, some targeted abilities, skill shots, and even auto attacks can still hit. Examples of this are singed fling being used at the same time the person flashes can cause the person to be flung back even after the flash finishes. Similar interactions exist between ahri's charm, other abilities, and auto attacks.