Can you take the end decor panels off, install the floor, trim the decor panels and then replace them? Otherwise I'd consider treating them in the same way as you treat skirtings and door casings, i.e. undercut it and run the flooring beneath it (hire a jamb saw or use a multitool). The weight of the carcasses should be carried by the feet under the units and you obviously won't be cutting any of those. Any cut MFC or MF-MDF edges at floor level will need to be protected in some way, maybe by painting the cut edges with gloss paint or some form of lacquer, but also I'd back that up by adding a bead of silicone to protect the edges at floor level
MFC - Melamine-Faced Chipboard - the material that most kitchen carcasses are made from
MF-MDF - Melamine-Faced MDF - the material that many kitchen decor panels are made from.
Alternatives to include foil-wrapped MDF (where a thin layer of printed paper and plastic are glued to the outside face) and vinyl-wrapped MDF (where a thin layer of coloured PVC plastic is glued to the outside face). For the purposes of this approach it acts in the same way as MF-MDF and needs any cut edges to be protected
