Floating LM317 (used at high voltage) protected by two Zener diodes
As per the LM317 data sheet, the max input-output voltage differential is 40V. This is why a 39V zener is placed across the device because, when 100V is first applied, the output is zero volts and therefore the zener rapidly charges the 100uF but maintains 39 volts across the device as a limit. Having said that I think 39 volts is a poor choice and I question its efficacy however, this is what the author of the circuit did intend I believe.

As for the 5.6 v zener, well the normal running voltage between output and adjust pins is 1.25 volts so clearly a 5.6 v zener is not going to be a problem to normal operation so, I would also say that this diode is here to limit voltage across these pins although the data sheet doesn't appear to state a maximum rating for this voltage. However, it's not uncommon to apply normal diodes to these positions to prevent another problem. See this: -



The diodes above are to protect the device from input voltage shorts when the output capacitor is fully charged. See also figure 24 and figure 37 of the data sheet for this information.