  We performed high-pressure transport studies on the flat-band Kagome
compounds, Pd$_3$P$_2$(S$_{1-x}$Se$_x$)$_8$ ($x$ = 0, 0.25), with a diamond
anvil cell. For both compounds, the resistivity exhibits an insulating behavior
with pressure up to 17 GPa. With pressure above 20 GPa, a metallic behavior is
observed at high temperatures in Pd$_3$P$_2$S$_8$, and superconductivity
emerges at low temperatures. The onset temperature of superconducting
transition $T_{\rm C}$ rises monotonically from 2 K to 4.8 K and does not
saturate with pressure up to 43 GPa. For the Se-doped compound
Pd$_3$P$_2$(S$_{0.75}$Se$_{0.25}$)$_8$, the $T_{\rm C}$ is about 1.5 K higher
than that of the undoped one over the whole pressure range, and reaches 6.4 K
at 43 GPa. The upper critical field with field applied along the $c$ axis at
typical pressures is about 50$\%$ of the Pauli limit, suggesting a 3D
superconductivity. The Hall coefficient in the metallic phase is low and
exhibits a peaked behavior at about 30 K, which suggests either a multi-band
electronic structure or an electron correlation effect in the system.
