You would need to go via a DVB-T dongle as the FLARM chipset is different to the Bridge, so the format of the RF packets are not the same.
Remember that the FLARM RF stage runs a very low power of 10mW with a stated effective range of 3km-5km. Using a DVB dongle for this will work, but with such low powers it doesn't take much interference/noise to swamp a signal. Within the FLARM they have filtering on the RF stage to help reduce this and use dedicated hardware akin to the Bridge to handle this.
Flying at a closing speed of 120kts, 3km gives you around 48s warning, at 5km this increases to 1m 21s, assuming detection is immediate but you could probably drop 10s-15s off those to ensure you have a series of received packets to do some processing with.
For Mode-S detection Lee compares known distances from other transmissions to assist with the bearing less targets, with FLARM what is there to compare to? Unless you just alert on every detection given the short range. Of course if you decode the packet you have the position of the FLARM transmitter and could take action as appropriate, but then sit back and wait for the lawyers to get involved.
Has anybody asked FLARM to produce a suitable dongle - at an affordable price as the hardware is almost free?
FLARM sell an OEM radio module for integration into other systems, pricing is on request under an NDA but I doubt it would be cheap (probably £100-£200 ish) plus the need to manage it's firmware updates too.
PS: Doesn't FLARM also use a frequency hopping RF system? Seem to remember reading that somewhere.