There are commercial UHF RFID tags implemented on flexible plastic materials. According to measurement of the permittivity of those materials, it seems they are PTFE-based. However, a major problem of the existing materials is that they are thin, which places a challenge to narrowband patch antenna.
Besides, according to the info provided by a plastic supplier, if high permittivity is not required, the hunt for the flexible plastic material will be easier.
Last but not the least, there is an article published on a recent issue of IEEE Microwave Magazine. It presents a method to generate a flexible material by mixing ceramic and polymer. The advantage of this artificial material is that it can deliver a high permittivity while maintaining the flexibility feature.