Can I switch iPhone SIM card into a old flip phone?

I have an iPhone 5c and I have been running out of data and to not go over my limit I was wanting to use my old flip phone but the switched the SIM cards to a smaller size so I'm not sure if I can still use that SIM card in my old phone?

You could just turn off the cellular data if need be. No need to switch SIMs.

You'd need a nanoSIM adapter to size it up for use in older phones that still use miniSIMs.