Buck Converter Multiple inductors
I would send a technical question to the pros like the engineers at Wurth Elektroniks and see what they say. 

The parallel inductance still needs to be what you want, plus the current ratings and saturation combined. So if you need 10A, assume +30% ripple current during pulses etc, so perhaps get 3 extra-low profile 5A rated inductors which in general should be smaller (in height). I found something interesting on the interwebs: 

Two separate 2.5-A, 22-µH power inductors are better than one much larger 5-A, 10-µH inductor because their collective volume is smaller than the volume of the single inductor by a factor of 2 . This minimizes overall component height. Source, last paragraph 

If you have no issue with surface area of the footprint you can probably find some reasonable inductors to lay out in parallel to get the current-carrying you need.

For 1.3mm or less, I found some on Digikey with parametric searching for high current and the seating height, and the best I could see where the Panasonic ETQ-P1W2R2WFP, 2.2UH @ 100Khz 3.4A 77.3mOhm Link.  If you need lots of inductance this will surely be awkward to put 3 of these in parallel, and even putting 2 in series, then 3 of those in parallel for a total of 6 inductors would be a very low profile and still only just good enough inductance for switching converters using frequencies up in the 1+ MHz range. That solution would take up about 160mm^2 of PCB space just for the inductors in the block like that. 

Multiphase synchronous buck converters often have multiple inductors on the output, but they are obviously switched at different phases so perhaps the magnetic fields do not affect each other as much. Finding a shielded inductor at the size you want is unlikely. I say you should do a prototype of just the power circuit and do some series testing if you have the time and money - testing for various loads and response to transients within the bounds of your final application. 

If it works, tell us all the results! There is not much information about this kind of application online, so for the purpose of the EE.SE Q&amp;A style forum, if you can prove that it operates effectively it would be good for you and us to hear about the results.