I have inquired about this with the company. They stated that any power source that outputs at least 1amp will power the camera. However, you need a power bank that is “Always On.” Majority of the power bank in the market has a over charge feature which when the device doesnt need charging, the power bank will turn off. So you need to go look for a power bank that has a feature that’s "Always On."
In amazon I found one from Voltaic. It has a feature that gives you the option to be always on.
Also, Anker makes power banks that outputs at least 1amp providing the device is always drawing at least 60 milli amps.
So basically, the blink camera will only take a power source that is always on or always outputting at least 1amp.
Before you buy a power bank make sure you inquire with the company and ask if it us always on or have constant output power of at least 1 amp when a device is plugged into it. Hope this helps. Goodluck!