Best short, info-dense description:
Hirose DF40C Series 100-position 0.4mm-pitch vertical SMT board-to-board plug connector, double-row, 0.3A/contact, 50V, 1.5–3.0mm mated height.
Shorter catalog-style version:
CONN BTB PLUG 100POS 0.4MM SMD VERT DF40C
I’d use the first one for Flux because it is compact but includes the most useful engineering specs.