Basically the order depends on what you want to use the gapclosers for.
If you want to chase someone you want to have all 3 procs of her Q on the enemy (so E-Q-Q-Q) but if you wanna get away you should use Q first because usually you will need your shield to absorb the incoming damage.
However if you just want to get as far as possible over a long time your order will be (R)-Q-Q-E-Q. Why? Well let me explain.
Your cooldown of Q will stay the same all the time (13s normal, 2.6 URF). Another thing for your Q is that the cooldown starts on the first cast and not like many other spells on your last. This means if you use Q-Q-E-Q you can use your Q again about 0.75 seconds after you finished that combo (not sure about the exact time but you get it).
Your E cooldown is at 10s (2s URF) at rank 1 and goes down for 1s (0.2s URF) for every rank. This means maxed you will have 6s (1.2s URF) cooldown. this also allows you to basically use it every time it's up again with this Rotation also because the animation of her E is a tiny little bit slower than the Q animations.
Now your Ultimate is also quite fun. At lvl 16 you have a 100% uptime (at 11 you have 3s CD) so it's really worth to use it all the time because it increases your spell/attack and jump range. (Cooldowns: 130/90/50 normal , 26/18/10 URF)