How to run electrical wire in concrete under the tile
FMC &quot;flex&quot; isn't allowed in concrete. In 362.10 ENT (smurf) is allowed to be embedded in concrete, so I think it would OK, but the inspector could have issue with meaning of &quot;embedded&quot; with such shallow cover, which could be  up to interpretation of &quot;similar finish&quot; by AHJ.

NEC 300.4(F) Cables   and Raceways Installed in   Shallow Grooves.
Cable or  raceway-type    wiring  methods installed   in  a   groove, to  be  covered by  wallboard,  siding, paneling,   carpeting,  or  similar
finish,   shall   be  protected   by  1.6 mm  (1∕16   in.)    thick   steel   plate,  sleeve, or  equivalent  or  by  not
less  than    32-mm   (11∕4-in.)  free    space   for the full    length  of  the groove  in  which   the cable   or  raceway
is    installed.
Exception No. 1:
Steel plates, sleeves,    or  the equivalent  shall   not be  required    to  protect rigid
metal conduit,    intermediate    metal   conduit, rigid  nonmetallic conduit,
or    electrical  metallic tubing.
Exception No. 2: A    listed  and marked  steel
plate less    than    1.6 mm  (1∕16   in.)    thick   that    provides
equal or  better  protection  against nail    or  screw   penetration shall   be  permitted.