I'm a writer the main character in my novel is a detective for a
sheriff's office in a Florida County. If this detective needed files
that were housed with a private company in another county how would
they go about getting a warrant for those files?

He would probably ask the court to issue a subpoena rather than a warrant.

Fearing that the files would be destroyed if they knew the authorities
were interested in them, the detective hires a professional burglar to
break in and get the files.............