This comment is aimed at the OP, but could be interesting to consider for anybody else in this discussion, despite its length. Stranger things have happened.
Parkour, as described by David Belle, is primarily concerned with your ability to react in an emergency. David identifies heavily with the MN motto "be strong to be useful", meaning that we aim to develop and cultivate strength (mental and physical) so that we can help people (including ourselves) in sticky situations. David said to imagine that you are in an emergency and then you will know what parkour was meant to be. With this in mind, here's what I want to add.
From the very beginning, a key aspect of training which will guide your direction and how you are seen by the community is your sense of priority. In descending order, what are the most useful skills to have in parkour which will equip you to deal with emergency situations (and by extension, life in general)? Before you even lay a finger on a railing or jump between two walls, you need to think about what is most fundamental to your ability to be useful. In my opinion, the basis for all training should come from general fitness. You should learn how to run for distance and how to run for speed, you should develop your muscular strength and your muscular endurance. This is more important than any "techniques" or "specific" training you can do. Why? Because by building a foundation of strength, stamina, speed and endurance, you give yourself a wide base which you can go on to use in all other situations.
With a physically fit body, you can now run farther and faster than the average adversary, you can move your body weight and carry heavy objects, but most importantly you are healthy (it would be worth mentioning that along with the training, good nutrition is also fundamental to your ability to be useful. As is rest). If you have ever seen Dogen Trick's "Titanium Ankles" video, you'll also know that with a solid foundation of strength, you can reap the benefits of more specific training faster than somebody who is only interested in the technical aspects.
Anyway, once you can run and have decent strength, the next most important abilities to have in an emergency tend to be those which involve obstacles other than flat ground. Sometimes it is inevitable (or just easier) to pass certain obstacles that lay in your path. In terms of a chase, the ability to climb quickly is generally the best skill to have. If you can get somewhere where you can't be followed, this is helpful. The obvious example is a roof. Sometimes it can be a flight of stairs or a mobility ramp that gives you the edge. It could simply take one turn vault to drop and roll. In any case, most situations will rely on a very general ability to run and overcome obstacles. Therefore, your training should be general and broadly applicable.
As you develop a strong repertoire of movements that help you in most situations, you'll want to begin to apply them. What I mean is, it doesn't matter that you can cat pass the wall outside your school if, after running for only 800 metres, you haven't the energy to get over it and instead take a longer, less effective route (and possibly come to regret this). This is where general fitness comes in. Your cat pass practice is probably pointless unless you know that you can use it when it comes down to a situation where you must. The likelihood of a situation requiring only a single, isolated cat pass is, after all, very low.
Once you have confidence in your abilities here, you'll want to expand to other aspects of training. What good is it to be able to reach a place if, when there, you are unable to help? Self defence, first aid and the ability to carry are likely skills to be required in these cases. Also, what good is it to be wonderful at level arm jumps if you find yourself on a camping trip and are unable to traverse mountainous rock to escape a wild goat-gone-crazy? (Shame on me for using such a dumb example.) Or are unable to swim a short distance? As you progress in parkour, these widely applicable skills become very important to consider.
There is much more to consider at this point. Your ability to surpass fear, to commit at height, to keep a clear head, to balance well. Many practitioners concentrate mostly on the fear aspect, practising bigger and more daring (and dare I say " coincidentally impressive") moves, jumping between roofs, making huge cat pass precisions and wall gaps. I think in some cases (or if I'm going to be daring, most cases), this over-emphasis on adrenaline-packed fear breaking is laced with egotistical motives. While surpassing your fears is utterly vital to your training of parkour, it should never be placed above your ability to run for example (and lets admit it, how many of us can do a big sdc-precision but are unable to run for a simple 3 miles?)
Now, lets consider flips. So far, I am only aware of a modest handful of situations in which a flip is the most efficient option. It can be used in a very specific situation and generally only if you have a high energy reserve to spare. As such, what grounds have you for practising flips more consistently than your ability to run? The point that I am trying to make is that flips come near the end of a very long list of descendingly fundamental skills. If you wish to be a truly great traceur, you should realise that in concentrating on flips, you are exploiting an incredibly narrow set of situations and will likely find your leg being chewed on by a wild dog when it comes to a real situation if you haven't already practised your fundamental skills to a high level. As I said from the start, it's about priority. As David Belle so rightly said, when you put yourself in those situations, you come to know what parkour really is.
Just to add a final few points, I think that the argument "flips help spatial awareness hence are good for parkour" is slippery at best. Personally, I haven't found the full-twisting back flip to have much carry-over to anything besides other flips (for others this may not be the case). I would contend that you'll get a better appreciation for precision jumps by practising them repetitively and diligently than by getting used to the feeling of being mid-somersault. DaveS made what I believe to be a better case for flips- the exploration of your body and its capacities. Although, I would still argue that you can appease your appetite for exploration simply by expanding yourself with the fundamental practises of parkour and without need for flips until you reach a certain (moderately high) level.
And that's all I have to say on the matter! I could have just said "it's about priority and what is most useful in the widest set of situations" but I felt like substantiating it and hope that I made a good case for my argument. I hope this is helpful.
