C172 CFI'S LANDING LONG DUE TO BRAKE FAILURE; DEPART RWY TO AVOID C340 LANDING BEHIND THEM.

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WE NOTICED BRAKE FLUID LEAKING FROM R MAIN LNDG GEAR ON GEAR EXTENSION. WE NOTICED NO PRESSURE ON THE R BRAKE PEDAL WHEN DEPRESSED. WE ADVISED OVER CTAF THAT WE WOULD BE EXECUTING A LONG LNDG DUE TO BRAKE ISSUES. WE SPECIFICALLY ADVISED THE C340 FOLLOWING US ON THE 45 DEG LEG TO DOWNWIND THAT WE WOULD BE LNDG LONG. UPON TOUCHDOWN WE VERIFIED THAT WE HAD ZERO BRAKING ACTION AND PERFORMED A NO BRAKE LNDG. WE WERE ABLE TO SLOW TO TAXI SPD WITH 1700 FT OF RWY REMAINING. APPLYING R RUDDER PEDAL ONLY HAD LITTLE EFFECT OUR DIRECTION CTL; SPECIFICALLY R TURNS. WE ELECTED TO CONTINUE OUR ROLLOUT TO THE NEXT TXWY TO MAKE A SAFE EXIT FROM THE RWY. WITH ROUGHLY 1600 FT REMAINING WE HEARD A FLT INSTRUCTOR JUMP ON FREQ AND ALERT THE C340 'TWIN CESSNA GAR! GAR! THERE'S A PLANE ON THE RWY!' BOTH I AND THE OTHER CFII/MEI-RATE PLT FLYING WITH ME TURNED AROUND AND SAW THE C340 ALREADY ON THE RWY ROLLING OUT ON LNDG; ALMOST ABEAM THE MID-FIELD TXWY. WE APPLIED PWR AND WERE ABLE TO TAXI INTO THE GRASS BESIDE THE RWY AS THE C340 ROLLED PAST US; COMING WITHIN 20 FT OF US. HAD ANOTHER INSTRUCTOR NOT BEEN WATCHING OUR LNDG AND HAD WE NOT HAD A REAR-VIEW WINDOW; I HAVE NO DOUBT THE C340 WOULD HAVE HIT US OR HAD TO DEPART THE RWY AT HIGH SPD CAUSING SUBSTANTIAL DAMAGE AND/OR PERSONAL INJURY.