I recently worked on a project to read the RFID tags. The project used the Devices from manufacturers like Zebra (we were using RFD8500 ) & TSL.
More devices are from Motorola & other vendors as well!
We have to use the native SDK api's provided by the manufacturer, how it works is by pairing the device by the Bluetooth of the phones and so the data transfer between both devices take place! The programming is based on subscribe pattern where the scan should be read by the device trigger(hardware trigger) or soft trigger (from the application).
The Tag read gives us the tagId & the RSSI which is the distance factor from the RFID tags!
This is the sample app:
We get all the device paired to our Android/iOS phones :