Getting a legacy Uno to talk to any device in the Particle ecosystem isn't the simplest thing to do. If you could swap out the Uno, that would be best. It doesn't have to be bluz, it can be a Photon or Core or any other device that talks to the Particle cloud. It is very easy to send data to/from other Particle devices, much more of a challenge to do it with devices outside of the ecosystem.
If you didn't want to use the Particle cloud, using two bluz DK's connected to one gateway would also work. You could use local communication so they could talk to eachother.
It wouldn't be so straight forward to try and get bluz to talk to an Uno through BLE alone. While possible, it would require you to delve into the BLE specifics.