The Kylin is perhaps one of the least understood pieces by beginners. First, here is a reminder of what it looks like:
and here is how it moves:
Beginners tend to overrate the Kylin because of its potential to promote to a Lion. In particular, you should consider it a little weaker than the Phoenix. Note that 81Dojo gets this wrong – it rates the Kylin as stronger than the Phoenix.
First, ignoring the promotion possibilities, the Phoenix is stronger than the Kylin, because the former can potentially occupy any square on the board, whereas the latter can only ever occupy half the squares on the board. Here is a diagram that illustrates this:
Since you should always promote this piece when entering the promotion zone, the diagram only illustrates the squares outside the promotion zone, plus the potential promotion squares. Other theoretical positions are not interesting.
Regarding the promotion. Although the Lion is by far the most desirable piece to have, a second Lion is worth less than the first one , at least when the opposing side has a Lion. This is because one Lion defends against two Lions nearly as well as it does against one. If the defending Lion is protected, it doesn’t matter how many attacking Lions there are, none of them can capture the defender. It is for this same reason that giving 2 or 3 Lion handicaps is practical for the stronger player.
Another factor is that it is easier to promote the Phoenix then the Kylin (because it has twice as many possible promotion squares).
Yet a third factor is that by the time promoting the Kylin becomes a practical possibility (i.e. they are few pieces left on the board), the value of the Lion has decreased to almost that of the Free King. And if your promotion is to get a second Lion (rather than a replacement for a previously captured Lion), the Free King has more targets to attack.
So even taking the promotion prospects into consideration, the Kylin remains weaker than the Phoenix.
Because the promotion prospect is not so tempting in reality as beginners think, it is a reasonable strategy to use the Kylin as an attacking piece in the open, and this is quite common in strategies that involve deploying the Dragon Kings to the squares immediately in front of the King and Drunk Elephant. Do not hesitate to exchange your Kylin for a Phoenix, Bishop, or Vertical Mover. (Exchanging it for a Side Mover is another matter, as one of the principle tasks for a Side Mover is to prevent a Kylin from promoting.)
The more usual deployment though, is close to the castle, as it’s ability to jump over the defending generals makes it a useful reinforcement. Jumping laterally twice from the initial square is also sometimes seen, as it can be a useful extra defender for a flank that is coming under attack. This is also the best starting point for a promotion attempt in the endgame.
If you still have your Kylin in the endgame, then the best strategy to attempt promotion is to jump out to the side on which your opponent has fewest pieces (and especially the side from which the opposing Lion is absent). And then jump straight forwards towards the promotion zone. This works particularly well against the computer program HaChu, as it cannot see your intent until you start to jump forwards. So it cannot prepare defences against the promotion.