Yes it’s a good idea to wear eye protection when using a UV flashlight. Any polycarbonate safety glasses should work.
I have a Convoy S2+ UV flashlight and in the past not used eye protection and by accident shined it against something shiny. No eye damage, but I could feel it afterwards. It’s similar to wearing eye protection when working with power tools. You don’t expect anything to happen, but if it does, you’re glad you protected your eyes.