While you may find "Nike+ FuelBand app download" links on third-party APK mirrors or archive sites, they will not work as intended for a few reasons:
The Nike+ Connect desktop application for Windows or Mac was the primary way to manage the band via USB. Some users report it can still be used to set the time on the device, even if it cannot sync data to the cloud. nike+ fuelband app download
The software was built to communicate with NikePlus servers that were shut down in 2018. You cannot sign in or sync new data. While you may find "Nike+ FuelBand app download"
Your historic NikeFuel data is no longer accessible, though running data from the same era was often migrated to the Nike Run Club (NRC) app. How to Sync a Nike FuelBand Today (Legacy Solutions) You cannot sign in or sync new data
The original was officially retired by Nike on April 30, 2018, and is no longer available for download from the Apple App Store or Google Play Store . Because Nike also shut down the backend sync servers required for the device to function, the physical FuelBand is now largely non-functional for its original tracking purposes. The Current Status of the Nike+ FuelBand App
If you are determined to use the device, your options are extremely limited:
Since the FuelBand ecosystem is defunct, most users have transitioned to modern fitness apps that offer similar social motivation and "gamified" activity tracking: Best Nike Fuelband alternatives - CNET