Over voltage protection for a buck controller 24V in. 4-5V out
The IC we use has a tenancy to cause over-voltage spikes, destroying the LOAD LED Display Drivers when accidentally touched by engineers,


If properly designed and constructed systems based on that IC should be "well enough behaved".  "Touching" needs to be defined - and what it is equivalent to understood.  

If "touching" literally means touching the equipment with a finger then it is clearly marginally stable and the design and/or construction need to be reviewed. 


  Could I stick a Zener diode to clamp any over voltages to protect the load from over voltages?



A small capacitor across R2 (maybe 100 pF - 1 nF - but experiment and observation may be needed) should improve transient response and reduce spikes.
If the spikes are of limited duration a zener like clamp may help. However, the device that you specified is rated at 1 Watt maximum. Your system can produce up to 5V x 15A = 75W, and while all of that would not appear in a clamp, much of it may depending on the nature of the "spike". A simple and as robust as you wish to make it clamp can be constructed with a voltage sensor and clamp transistor. This could be as simple as a MOSFET (or bipolar transistor) with resistor in it's drain across the Vout line and a zener from Vout to gate with a gate pulldown resistor. You would have to design it to survive power dissipation during a "spike", adequately fast gate turn on and off time.
Use of a simple overvoltage sense amplifier / comparator would improve FET gate drive conditions. IF the FET is switched on and off rapidly dissipation can be mainly in the drain resistor and you can design it accordingly.


BUT the better solution is to fix what is clearly a marginal design - and perhaps teach your engineers to keep their fingers out? :-)