3/8" FMC has very limited allowed uses in the NEC and when allowed it will have restrictions as to what you can use it for, not only does it have to follow what is required in 250.118 as was pointed out but also 348.20(A)(1)-(5) to which feeding a receptacle is not listed.
Also if we look at 348.60 if flexibility is required after installation then you have to install an EGC if this soup warmer is expected to be moved for cleaning which I think it will be, the problem can be if you use fittings that fit inside the 3/8" FMC then you are limited to just 2 #12 thhn/thwn conductors (table 348.22) which can be a problem installing an EGC so make sure you use connectors that go on the outside of the 3/8" flex so you can install an EGC.
Even with fixtures I have always installed an EGC, after seeing some 3/8" flex light up like a heater element from a short in a fixture it kind of scared me and I have always installed an EGC since then, but code does allow it to be used as an EGC on circuits up to 20 amps as long as flexibility is not expected after installation and listed connectors are used (250.118(5)a.)
This is about the best I can narrow the NEC requirements down of the limitations of using 3/8" flex in your installation, the end results will be up to your inspector.