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Equalizing for equal loudness of sines does not give you a perceived flat frequency response.
Correct. You absolutely DO NOT want to equalize out your equal loudness curve. That curve set is built into human hearing, you don't want to equalize it out, and besides, it's level dependent.
The curve you'll get from this test will be the equal-loudness response of your own hearing with the mask of the response of the headphones/IEMs you used for the test. The results are pretty meaningless and not useful at all for setting an equalizer. At best the results present something that is of interest to look at.
The target response curves of the three types of headphones plus IEMs are all different, but none are flat, and certainly none are related to the equal-loudness curves. Headphone target curves are there to compensate for the difference in the way sound is presented to the hear by headphones vs a free field.
You can experience highly accurate and detailed headphone EQ with the Audyssey "amp" app, and some of the others. Audyssey also features their dynamic EQ, which compensates for the effect of the change in hearing response at low levels relative to the spectral balance at the level at which music is mixed.
Using an equalizer to compensate for an individual's hearing difference is also not a great idea because every individual has a build-in established "normal" based on every-day hearing. Attempting to compensate for a deficiency, unless large enough to be considered a hearing loss, will always result in unnatural balance because of its contrast with what's heard in life. It's for this reason that people who have hearing aids prescribed are encouraged to use them all day, every day, or they will always sound "wrong".