Rumble's Skill Max Order: Q → E → W
Matchup Tip: If Rumble overheats, instantly run him down because his Overheat lasts for 6 seconds, which prevents him from being able to use any abilities
Level 1: Quinn Cheese from the bush and then side step instantly to juke his E. He gets two stacks, so your goal is to side step them if you can after you E. If he misses both, you get a window to run him down. If he lands them, you will be slowed so you cant trade much after. Keep in mind that his E is a 6 second cooldown, and so he can use it on you freely. If you stand behind minions he can't hit you with it.
Level 2: Rumble will need to use Q to keep up with your push. Do not fight Rumble when his Q is active because it is longer than your AA range, so you will fight in his fire if you trade with him in his Q.
Level 3-5: How you play the trades is to push for prio in this lane, and this will force Rumble to use Q on the wave to match with your waveclear. The second his Q is down, instantly vault him to go for a trade. You want to try to side step his Es if you can, but regardles you win the trade when his Q is down. Take short trades like these and the lane will be more bearable.
Level 6+: His R is terrifying, especially if he's fed in lane. Look to slow push the wave and go for a roam if you see an opportunity, otherwise it is vitally important to not take bad trades becasue if you are low then he will be able to 1 shot you. If he Rs you, hope that he walks to you in melee range so you can vault on him to escape. I like fleet in this matchup for the sustain and movespeed to help escape his R when he launches it. Nul Orb works wonders for this reason as well.
I put the matchup as hard because to inexperienced Quinn players, Rumble will bully you quite heavily. However, when you learn the matchup I place it at medium difficulty.
First, understand how Rumble's passive works. When Rumble's heat is above 50 (over half), his abilities are empowered, which means all of his abilities and their effects will be 50% stronger.
However, if Rumble's bar becomes RED, then he will be silenced for 6 seconds, but his auto attacks will be stronger if this is the case.
If Rumble ever goes red, then hit him with a nuke because he will be rendered useless for 6 seconds since he is a melee champ who cannot use abilities.
Now, if Rumble is yellow, play back because his Q will burn you alive. How to win the rumble matchup is to WAIT for Rumble to Q the wave.
As an ADC top laner, we can control the wave with our AAs only, and so we can push if needed without using abilities. Other champs like rumble must use their abilities if they want to match our push to freeze the wave, so he will use his Q quite often to push the wave and harrass.
Rumble Q is 600 range, so play extra fat back because it outranges your auto attack range. Save your abilities (though you can Q the wave if needed, just save vault always).
When Rumble Q is Down, INSANTLY go for a huge trade on him and proc your PTA as well. You can weave Q and your autos, along with E for a big, big trade. Rumble only has his harpoons up, which don't do much damage when his flamespitter is down. Keep mimicking this, and you will find that you will hard win the trades.
Post 6 is scary, but just make sure not to take dumb trades because he often can't 100-0 you in lane. He'll need to poke you down first, and then finish you with his R all in combo. But, if you play the lane like I suggested (stay back, wait for him to Q wave, then engage after Q is down), he won't be able to get you low ever enough to combo you.
Play confident, and his Es are sidesteppable, especially with your harrier proc MS too.
I don't like building hexdrinker early, but if you need to, then run along with it.
Nul orb is critical in this matchup.