No, there is no Florida income tax for a flow-through entity for you to file. They have a corporate income tax, which you are not required to file.
Here is more information about the Florida Income tax: Who Must File?
Based on the information you provided, you are not required to file this and thus have no Florida obligation. Only S-corporations that pay federal income tax on Line 23c of Federal Form 1120S must file a corporate tax return in Florida. Single-member LLCs with an individual single member don't have an obligation.
