Two 240-12 V wall warts in parallel through LM2596 buck regulator to increase available current
Putting power supply voltage outputs in parallel is not ideal. One device will always win i.e. it outputs 0.1 volts more than the other and the lower output supply will just shut down its output stage thinking that it has to find a way of lowering the output voltage.

My advice would be to connect them in series to produce ~24V then use a buck regulator to give you 12V. The maximum current into the buck will be limited to the lowest current but, even so, with an efficiency of maybe 90% you should easily get 2A from the 12V buck regulator.

Another consideration is what happens when one power supply is disconnected from AC. If in parallel you may stand a chance of damaging one or both. In series you can use bypass diodes to prevent this happening plus you have the voltage overhead to suffer a diode drop or two without breaking into a sweat.


  My plan was to take these two power supplies and hook them up to an
  LM2596 buck regulator circuit in order to increase the available
  current.


This is madness and makes no sense. If the wall-wart(s) produce 12V then why bother with a buck regulator - the LM2596 needs a couple of volts higher on the input than the output anyway so your idea about 12Vin and out is fallacy. Read the DS.