What should I be building on top Rumble? I feel like when I build pure AP I die when I try to flamethrow the other team. So what do I build to actually survive with flamethrower? Or should I just use Q and run?
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Hextech Revolver (helps a lot with lane sustain, can upgrade to WotA later if your team would benefit)
Tabi / Mercs / Sorceror's - depends on your needs really. If you're doing perfectly fine you can get sorc's, but I usually go for mercs. You can't stick to the enemy if cc's being used. You might need tabi though against a lot of AD.
He does have a general build, but honestly from here on it depends what you need. If you're feeling too squishy like you mentioned in your post you may want to get a defensive item next. Abyssal Scepter, Zhonya's Hourglass, Rylai's. Rylai's is very good on Rumble for obvious reasons, and synergizes well with Liandry's Torment, another great item for him.
A typical 6-item Rumble will usually include:
Mercury's Treads (/Ninja Tabi / Sorceror's Boots) Will of the Ancients Rylai's Crystal Sceptre Liandry's Torment Rabadon's Deathcap Abyssal Sceptre Zhonya's Hourglass Void Staff
A good general Rumble build is boots+Liandry's+Abyssal+Zhonya's/Randuin's/Sunfire(Zhonya's for more killing power. Randuins for more armor. Sunfire does give health+armor but almost never as good as Randuin's)+Rylai's+Deathcap/WoTA(you almost always would prefer Deathcap).
I do like getting an early Hextech whether I am building WoTA or not. Boots can be Sorc/Tabi/Merc's. Completely your choice.
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