You are finding 3 places.
Also, Kiribati's flag is for checking if you got the "places" correcct.
Hint 1:
Kiribati's flag has water in it. Its useful.
Hint 2:
Fixed version:
Hint 3:
What does Azerbaijan and the Netherlands have to do with water?
Hint 4:
Think of elevation.
Last hint:
If Bolivia, Ecuador or Colombia was pointing to Kiribati's flag, It would be on top of the image.
Partial answer
I've got the countries figured out, but there's five of them (six including Kiribati), not three:
Big flag on the left:
KIRIBATI (I haven't even spoilered this since it's mentioned in the question).
Flags on the right:
AZERBAIJAN (internet domain .AZ, calling code 994)
NETHERLANDS (internet domain .NL, calling code 31)
Mottos below:
TUVALU (internet domain .TV, calling code 688). National motto "Tuvalu mo te Atua" = "Tuvalu for the Almighty".
SURINAME (internet domain .SR, calling code 597). National motto "Justitia – Pietas – Fides" = "Justice – Piety – Trust". Interesting that only the last two-thirds of this is included; that must mean something, but I'm not sure what.
TURKMENISTAN (internet domain .TM, calling code 993). National motto "Türkmenistan Bitaraplygyň watanydyr" = "Turkmenistan is the motherland of Neutrality".
Possible method of answering (especially given the title):
something to do with the two-letter internet domains for these countries. Interestingly, Kiribati (.KI) is exactly a 3-letter Caesar shift from the Netherlands (.NL), but between them is not Azerbaijan but Macedonia (.MK). Meanwhile, Tuvalu is .TV and Turkmenistan is .TM.
By the way,
what I've got as Tuvalu could also be indicating TOKELAU (motto "Tokelau mo te Atua", but a territory of New Zealand rather than an independent state).
.tv domains.
$\endgroup$
[Not a full answer, only some loose thoughts that are too long for comments. I'm building on Rand al'thor's answer here. Edit: I've revisited this answer and have even more incoherent ramblings below. Enjoy!]
Flags
The flag of Kiribati features sine-like waves and a bird over a rising sun. Kiribati is an island state in the Pacific Ocean. Its territory (Mostly "aquatory", really) is known for spanning both the equator and the antimeridian, but not the international date line.
The small flags to the right (Azerbaijan and the Netherlands) point at the sea. Azerbaijan's capital Baku is the lowest capital of the world. It is on the shores of the Caspian Sea, which is 28 m below sea level. Parts of the Netherlands are also below sea level, in particular the inland bay of the IJsselmeer.
We are told to check the "three places" with the flag of Kiribati. A wavy version of the Dutch flag can be seen near the horizon of Kiribati's flag. Some of the flags of Dutch provinces, notably Zeeland and Overijssel, but also the polders of Flevoland, have wavy designs. The city arms of Baku also feature waves, but they are not sine-like, but pointy.
"Mo te atua"
Tuvalu mo te atua is the state motto of Tuvalu, an island state in the Pacific Ocean and nor far from Kiribati. What's interesting is that Tuvalu's coat of arms features a wave design like the one in the flag of Kiribati, albeit in gold and blue.
"Piety - Trust"
Justitia – Pietas – Fides is the state motto of Suriname, whose coat of arms also features waves, this time in blue and silver.
Ecuador, Bolivia and Colombia
The last hint mentions that those countries would refer to the top of Kiribati's flag. All three have coats of arms with a condor sitting on top of a shield, so like Kiribati's flag, they have a bird near the top. They are also in the Andes, which makes them places of high elevation. Bolivia is landlocked, but Ecuador and Colombia have sea coats, so they have points at sea level. (According to this list, they don't have significant points below sea level, though.)
Bitaraplygyň watanydyr
Türkmenistan Bitaraplygyň watanydyr is the state motto of Turkmenistan. Like Azerbaijan, it lies on the Caspian sea and therefore has parts below sea level. Unfortunately, its coat of arms has neither waves nor birds nor sunrises: Among other things, it features the crescent of Islam and the former president's pet horse ("a source of pride to the people of Turkmenistan") in realistic, not heraldic rendering. (But the country's second largest city Türkmenabad features some waves in an Islamic shield.)
ABCDEFGHIJKLMNOPQRSTUVWXYZ
That's the title. Surely it hints at something. I have no idea at what. (But I note the A–Z and that Azerbaijan's two-letter cpountry code is AZ. Rand has already pointed that out, too.)
You are finding 3 places.
We are looking for unspecified "places", so not necessarily countries or towns. I think that none of these places is a country mentioned so far, because its flag or motto is in the question. My guess is that we are looking for three places that share some characteristic with the countries already shown.
So far, we have seen a hodgepodge of rather heterogenous characteristics. Some proposals:
The British Indian Ocean Territory is the prime example for wavy water in heraldic designs. It is not the only place with waves in its coat of arms, though.
The Dead Sea is the Earth's lowest point on land and like the Caspian Sea and the IJsselmeer it is a body of water below mean sea level. In this puzzle, countries seem to be categorized by their lowest point. If that is below sea level, they are associated with the waves in Kiribati's flag, otherwise they are associated with the sky.
I can't think of a third candidate, which will probably be identified by a third characteristic. Perhaps it's just Mount Everest as the highest elevation or, more likely, Lesotho, which is the country with the highest minimum elevation.
But that doesn't account for A–Z or Turkmenistan. Well, I'm out of ideas.
After revisiting my answer – an upvote out of the blue had drawn my attention to it again – I think ...
... that common flag and arms patterns are a coincidence and that the whole point of the image is to get to a list of state capitals by elevation. Kiribati's and Tuvalu's capitals are at sea level; Baku and Amstardam, the capitals of Azerbaijan and the Netherlands, are the only ones below sea level. La Paz, Quito and Bogotá, the capitals of the Andes countries mentioned in the last hint, top that list.
(Now that I look at it, all hints are more or less about elevation. The common flag patterns exist only in the fantasies of my inner vexillologist.)
Kiribati was chosen, because it is at sea level and because the design of its flag features a clear water line and therefore lends itself to mark capitals as below or above sea level.
The whole alphabet in the title could mean that the "three places" must be determined from an alphabetically sorted list. Perhaps the first three capitals at sea level – Apia, Baikiri and Bandar Seri Begawan (the state capital formerly known as Brunei City) – are the answer? Well, there's not enough information to be sure.
I'll note that in the state mottos mentioned in the question, the first word is missing. Perhaps that means that the sorting must be done from the second letter of the state or its capital? Well, perhaps not; the omission is probably just there to make the countries harder to find, because in two of the mottos, the first word is the name of the country.
I'm still puzzled about the inclusion of Turkmenistan. At 215 m, Ashgabat is nowhere near sea level. In all avenues I have pursued in trying to crack this puzzle, Turkemistan was always the odd one out, Motherland of Neutrality or not.
