FireStick uses USB for power only. You might connect wired Ethernet by using OTG cable into the 'stick, then powered USB hub, then USB-to-Etherhet adapter, then cable to your switch. If you have only one Ethernet cable around, you can use a switch to "split" it.
ANother option is to use an old router turned into WiFi access point, close to the 'Stick. In that case you can use that router' builtin switch.