Calculating Slew Rate from a time-constant
There are too many problems with this design so the question becomes irrelevant until you become clear on the overlooked assumptions that nmatter.  

Slew rate, dV/dt is limited by output current
-      i.e. dV/dt=I/C for some given capacitance load.
- usually a comparator is used rather than an Op Amp.
- the hysteresis and thresholds are directly affected by output swing and positive feedback ratio of that swing.
- your design is referenced to ground so a bipolar supply is needed if using an Op Amp.
- the R3 value is assumed to be much larger than output impedance of driver 

Thus if 3*tau=500µs  then R3C1=500us/3=166us and R3 >> Rout and if Vout=5Vpp then the slew rate is always much faster and a transition time much less ( &lt;10% ?) than  your RC time constant.  Slew rate and latency are thus affected by your system requirements as well. 

But without that input, I would suggest a slew rate requirement of >5V/16us or >0.3 V/us which is easily doable by many IC's.  ( keep in mind Analog IC's are designed for many purposes with bandwidths from 25kHz to 500 MHz)