Triangle generator circuit - supply rail error
I have a simple triangle generator circuit soldered and powered by 5V
  rails


Given that you said "rails" and not "rail" AND that you said the output should be +/- 4.2 volts I have to assume you are attaching +/- 5 volts to the circuit. If you are then you have probably destroyed the LT1719 because it's maximum supply voltage (Vs to GND) is 7 volts and not 10 volts: -