The only way I know of is to use an LTE Apple Watch (you need an iPhone to do initial setup) and once setup is done, just use it standalone. Enjoy the horrible battery life and limited features though because even in standalone it has less than half functionality as one that's connected to an iPhone.
From experience, apps like Apple Pay, some parts of Health (notifications), Maps, system updates, digital touch won't work in standalone, or break after some time. (Apple Pay will work for x times then want to sync with an iPhone/Wallet app).
SMS, iMessage, Music, Phone, Fall Detection (SOS), Siri, HomeKit support, watch (obviously) setting Alarms, calculator, and others do work in standalone though. But battery life will be 1/3 what it normally is since the LTE radio uses a ton of it when always active.
An Apple watch is basically a flip phone in watch form in LTE only mode. As you already got a flip phone do you really need two?