This press release is quite misleading... the only novel aspect here is "flexible". It's less efficient than the existing rectenna solutions. And it's just as useless unless it's placed directly next to a WiFi router that is experiencing unusually high load.
A single AA battery can deliver 40uW for about 4 years, continuously.
Use a carbon zinc dry cell for things like that, they won't leak like other alkaline battery types. Bit lower capacity so you'll have to replace them more often but they'll not lead to destruction of the device either.