Yeah I agree that that specific section does seem to apply to people running businesses (with licenses), but I'd be willing to bet that any code enforcement would reference that law for backyard chickens, too.
It looks like 10 chickens are the maximum:
Sec. 27-282.25 specifies kennel, small (with kennel, large reading the same) as 1 - 10 chickens.
https://library.municode.com/fl/tampa/codes/code_of_ordinances?nodeId=COOR_CH27ZOLADE_ARTVISURE_DIV2RESPUS_S27-282.25KESM
also BYC has a specific section...
I live about 30 minutes away from Tampa, we can only have 3 hens, and no roosters.
I know someone up in Wesley Chapel (about an hour from Tampa) that runs a rescue, and has ducks, chickens, and the like. They're an educational facility, as far as I know. If you don't find anyone, let me know...