If you have a felony in Florida will it show up on a background check in a different state?

Yes. The States all share the same system.

I'm assuming this is related to your thread about extradition and they should be combined.

OK thank you

Yes, all crimes ( with the exception of some city code enforcement and city violations) are listed on a national data base. So it is available within seconds anywhere in the US. And available in many parts of the world within a longer time frame.
Example, in the US we police have access to Interpol ( Europe) criminal data base. But it is not instant.

Yes. The second your name and SSN are punched into any police computer anywehre in the USA your other felony will immediately show up. You can't hide anywhere anymore.

What if it was for a job in a different state

"Anywhere in the US" (quoting Twinkie) means "Anywhere in the US."

Got it?