Advice for using 60 watt peltiers. Is 12V 3A enough to get the job done?
There are a few problems with that setup both thermally and electrically.
Electrically there is the problem of connecting multiple 5V regulated battery packs in parallel to get the required amperage.  They were not designed for this and there is a likelihood that one will output slightly higher voltage and prevent the other from load sensing and staying turned on.  The peltier will be under powered.  There are at least 3 unnecessary regulators wasting battery power and generating additional heat in the area around the phone.  Just supplying a proper 12V battery without regulator goes a long way toward making this more viable and cleans up the wiring.
The peltier does not magically create cold from electricity.  It uses electricity to pump heat from one side to the other.  It generates 60W of waste heat in the process.  Where does all that heat go to?  Only a few mm away from where it was collected, on the other side of the peltier.  That puts all the heat right back into the air immediately surrounding the phone.  A fan and heatsink might help move heat a bit further away, but that is more power draw.  

The phone really needs to be inside an insulated container to keep it away from the heat.  And if you are going that route, why not just take a frozen ice pack with you, or drop in a cold can of soda from a store.  There could be moisture problems from condensation.  In a pinch, velcro the phone to a cold aluminum pop can.

If the phone can handle moisture, I might try to fashion a case or stand and sunshade from terra cotta.  Soak it in water and allow the heat of the day to evaporate the water cooling the terra cotta and anything within.