Any RFID reader that works in "keyboard emulation mode" should work just fine with FileMaker. Check the technical info and make sure it can also add data to that which is scanned. In keyboard emulation mode, you can set FileMaker up to respond to the scan via the OnLayoutKeystroke Trigger and OnObjectExit triggers. Thus, you can program the scanner to put a set of characters at the start of the scan to trigger a script that identifies the characters as the trigger for a new scan and puts the cursor in a field where you want to see the scanned data.
The same method can use characters at the end of the scan to trigger a script to process the data so scanned, or you can append a tab, enter or return character to the end of the scanned data and modify the field's behavior settings so that this character exits the field. Then you can use the OnObjectExit trigger to perform the script that processes the scanned data.