The Mechanics of Whirlwind Kick's Movement Technique
Effect: You fly your speed. The first square of this movement doesn’t provoke opportunity attacks.
Powers in 4e do what they say, nothing more nothing less. Thus you are free from provoking only for the first square of movement.
How to use whirlwind kick and avoid provoking
As you say, against one enemy you can use that first square to move diagonally up and back to leave their range and then fly where you want to go from there.If you have more enemies near you such as 2 flanking, the 1 square still help to limit it to only one opp attack vs multiple. Similarly, if you have 3 enemies adjacent and they are spaced out evenly there should still be 1 square that only exposes you to one opp attack.
Fluff has no bearing on mechanics
Fluff vs. crunch. Crunch are the rules, the parts of the power card that refer to the rules and the mechanics of the game. Fluff is any part of the powercard that is not crunch: the name of the power and the description of the power.
The descriptions of powers & items in 4e are simply that; no more, no less. The descriptions/flavor text/fluff printed on power cards has zero bearing on rules. Its there to make the power sound more fun, spice up the game, and/or help you visualize what the power is doing better.
Sorry, one movement only provokes one AoO from a given defender.
See the d20pfsrd:
If you have the Combat Reflexes feat, you can add your Dexterity modifier to the number of attacks of opportunity you can make in a round. This feat does not let you make more than one attack for a given opportunity, but if the same opponent provokes two attacks of opportunity from you, you could make two separate attacks of opportunity (since each one represents a different opportunity). Moving out of more than one square threatened by the same opponent in the same round doesn't count as more than one opportunity for that opponent. All these attacks are at your full normal attack bonus.
So if you shriek "SERPENTINE!!!" and run circles around your opponent, they still only get one "leaving a threatened square" AoO on you.
The opportunity from Hold the Line is different, but only works once upon them entering your threatened area. So you would get only one from Hold the Line and one for them leaving a threatened square.
Note that the leaving a threatened square is per round - not even just per turn - with the Mythic rules in use in our WotR campaign we've been finding a lot of cases where you get to act multiple times in a round, even charge multiple times, etc. If by hook or crook someone charged you, ran off, charged you again, and ran off again over the course of a round (on their turn or across multiple turns), you would still only get 1 AoO for them leaving your threat but could get multiple from Hold the Line, if they actually leave and enter your threatened area with a charge twice. Up to the limit of the number of AoOs you have.
Best Answer
From the PHB, page 195:
While there are certain things that modify this (like the Mobile feat, which I will explain further down), this is the trigger for an opportunity attack. In your example, none of what you did prior to moving out of their reach actually matters. If you were in their reach, and moved out, you provoke an attack of opportunity.
For your specific example, there is a feat for this exact scenario. The Mobile feat, from page 168, gives you, among other benefits, this:
So if you want to move in, attack, and move away again, you can, but it will require a feat if you don't want to trigger an opportunity attack. Note that moving away might not achieve all that much - if the monster has at least your speed - 5, they can still move after you on their own turn and attack you anyway. You might be better off staying in melee with them. Obviously, there are a number of reasons why this might not be true.