Don't expect me to give you runes and masteries because i'm not a pro
Rumble is NOT a BURST CASTER so you will need to keep a close distance with W and E for your FLAMETHROWER to be effective.
Rumble is recommended to solo top than going solo mid. You need brushes for better zoning.
SUMMONER SPELLS
IGNITE ; FLASH
SKILL ORDER:
Q-W-E-Q-Q-R-Q-E-Q-E-R-E-E-W-W-R-W-W
Depends if you are laning against a burst caster, max W instead of E
EARLY ITEMS:
BOOTS 3-4 HEALTH POTS ; HEXTECH REVOLVER ; (wards)
MID ITEMS:
MERCURY'S THREADS / BOOTS OF SWIFTNESS ; WILL OF THE ANCIENTS ; RYLAI'S SCEPTRE
LATE ITEMS:
RABADON'S DEATHCAP ; ABYSALL SCEPTRE ; WARMOG'S or FORCE OF NATURE or ZHONYA'S HOURGLASS
EARLY GAMEPLAY
As Rumble, you are the "bully" in lane. Zone the opponent out with your flamethrower constantly but watch your heat meter so it will stay above 50 Heat and minions WILL turn aggro on you so pay attention to that too. Once you zone him out, you should level up faster and MAKE THE MOST GAY HARASS possible. Q+W and E when opponent tries to run is enough to harass at level 3. Continue this zoning until you hit level 6. Don't forget to recall and get HEXTECH REVOLVER once you get 1200 gold.
MID GAMEPLAY
Once you recall and get your WILL OF THE ANCIENTS, you can sustain with all those minion aggros focused on you. Get your RYLAI'S if possible. You should be able to get kills right about now. Just ward your lane because you will overextend alot as Rumble.
LATE GAMEPLAY
Now it's time to carry teamfights. Predict where the teamfight will occur and ult their AP / AD carries and burn the hell out of them. If you are being focused, you can flash out with your W on, and shooting your E so they won't chase you (just don't miss).
ESCAPE LIKE A COWARD
Rumble has an easy escape mechanism. W and hit you E twice on a single target ensures your escape from him. BUT when getting ganked, W and hit your 1st E to the ganker and the 2nd one to the opposing laner can disable the gank. Ult your escape route if you are cornered.
P.S : you still have flash -_____-