Florida has not held a primary for statewide office for any party other than the Republican and Democratic Parties since 2016, when there was a Libertarian primary for U.S. Senate between Paul Stanton and Augustus Invictus. This year there will be a contested Independent Party primary for Governor. The two candidates are Reginald Byron and Michael J. Brown. Neither one seems to have a campaign website.
Technically, all qualified parties in Florida nominate by primary. But when only one candidate files, no primary is actually held and the person who filed is deemed nominated. Filing fees are so high in Florida that there aren’t many people who file to run in a minor party primary.
Before 2007, parties with registration below 5% of the state total did not have primaries; they nominated by convention. The law changed with HB 537.
No party in Florida history, other than the Democratic and Republican Parties, has ever had registration as high as 5% of the state total.