To ensure that all your equipment is recognised as a single aircraft, you must configure your FLARM device with the same HEX code as your transponder, and that the address type is set to “ICAO”
This allows SafeSky (and other systems) to correctly identify both devices as belonging to the same aircraft.
On a side note, it seems that your aircraft is actually equipped with Mode-S, which definitely explain the echo for yourself from FLARM:
Your transponder shipped with an official ICAO hex code 45E353. This one code must be configured on your FLARM device. You need to check your FLARM user manual to update the default code from DD4F96 to 45E353 and set address type to ICAO.