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Based on other questions it appears that a "flare" is always part of a healthy airplane landing.
This question asked when a flare should be started, and I found it interesting that the accepted answer expressed it in terms of altitude. Which got me wondering: Is the need for a flare a consequence of ground effect? And the optimal flare height for a particular airplane a function of when it enters ground effect?
It depends on the type of landing. If you are doing a normal landing on a normal runway, the round-out and flare are required steps to put you in a position to be in level-ish flight just above the runway (the roundout), and controlling the touchdown by trading inertial energy for increased lift by pitching as you feel for the surface (the flare).
Ground effect has an effect on the flare phase by giving you more energy margin if the ground effect is strong. So a low wing airplane with large flaps with a strong ground effect will have a lot more support from ground effect than a high wing airplane with small flaps that has weaker support from ground effect. If ground effect wasn't there, it wouldn't really change how you land too much, except you may tend to carry power into the landing more, or arrive with a bit more energy by increasing the approach speed a bit. In some airplanes the ground effect is much more pronounced than others (they like to float).
There are landings where you don't really flare at all. In an extreme STOL approach, you fly to the surface already in the landing attitude, controlling descent rate with power and maybe little pitch adjustments only as required for speed corrections. If the engine quits during such an approach close to the ground you are out of energy, already "flared" and will land hard and you live with that risk if you're doing that sort of thing.
And of course, there is no flare in aircraft carrier landings. You fly a constant descent into the ocean, and the carrier's deck just gets in the way of your descent.
Yes, optimal flare is related to the ground effect (i.e. must take it into account), but is not a 'consequence' of it.
In a way, it's the opposite. Flare does two things: primarily, it arrests your sink rate for a gentle touchdown, and also sets a correct attitude. If the airplane has a particularly strong ground effect, this effect will reduce your sink rate and 'cushion' your landing, without you doing much. There may be secondary effects though, which will require you to actively control attitude (pitch).
A case in point is Concorde. Due to its wide-chord wing and high angle of attack on approach, it had a very strong ground effect. So much so that it didn't require flare at all. However, this ground effect produced a strong pitch-down moment, which required the pilot to pull the yoke in order to maintain the attitude. As a result, the landing felt somewhat 'normal' for the pilot, except that the aircraft didn't pitch up and landed in the approach attitude.
The flare, or roundout, is performed as a part of landing in order to accomplish two things: 1) Arrest the rate of descent on the approach and 2) place the aircraft in the proper attitude for it to gently touch down on its landing gear. For tricycle gear airplanes, this is typically a nose high attitude so it will make contact with the runway on its main landing gear only. Critical to a good flare is arriving at the entry at the proper approach airspeed to minimize the float prior to settling onto the runway, typically Vref = 1.3*Vso + gust factor. This provides just enough energy accomplish your two flare tasks prior to the airplane being exhausted of energy and settling down onto the runway. Ground effect will amplify the time and distance covered during the round-out if the approach speeds are not correct, since it is reducing induced drag on the airframe, requiring longer times to exhaust the airplane of energy prior to touchdown.
The optimum height to begin the roundout depends upon the airplane in question, it’s approach speed, handling characteristics, etc. Typically small GA aircraft will begin this process at about 10-12 ft above the runway. Large transport category aircraft will begin this about 20-30 ft AGL. Just prior to touchdown the airplane will be approx 1-2 ft above the ground and in the proper landing attitude, if the flare was accomplished properly.
