How do I get compensation for a delayed flight?

I recently came across a site that supposedly automates this whole process ( https://www.getairhelp.com/en ). The article at http://henrikzillmer.com/justice-as-a-service implies that they gather data in an automated way from public data sources about the flight, so it's very hard to argue with it, and they send legally-correct notices to the airline. You may have some luck going with them, but I've never used the site so I have no idea how good it is.

How do you get compensation for this specific delayed flight? You don't because you're not eligible, and Easyjet is correct.

Looking at your link, the scheduled landing was 2035, with the actual landing 2354, a delay of 3 hours and 19 minutes. BUT the scheduled gate arrival was 2055, with the actual gate arrival of 2354: a delay of 2 hours and 59 minutes.

As per the Civil Aviation Authority's webpage:

The delay length is calculated using the time the flight arrives at its destination (this is based on the time at which at least one door of the aircraft is opened) — not the departure time.

^{emphasis mine}

Aircraft door opening sounds to me the same as gate arrival. This was under 3 hours late, and therefore you have no claim.

(NB I have also read Regulation EC 261/2004 which is the law which allows compensation. It does not define where the point of arrival is measured. I, personally, am happy to accept the Civil Aviation Authority as a source of authority for the definition. Note also that at the top of your flightaware link it states the arrival was 2 hours 59 minutes late, and so flightaware also seem to use this definition.)

It's an interesting to note that flightaware has both "landing" and "gate arrival" as 2354, I'd have thought that was a typo. Checking other instances of this flight generally only show a minute's difference, so it sounds plausible.