Flexographic printing, which involves high-speed contact of an inked stamp against a substrate, is of increasing interest for scalable manufacturing of electronics in new formats. However, the adaptation of flexography to thinner, finer features which are generally required for printed electronics requires improved understanding of stamp-substrate contact mechanics. Here, we present a desktop plate-to-roll (P2R) printing apparatus which enables the study of flexographic printing in a semi-continuous format that mimics industrial printing. In particular, we tailor the specifications of the machine to use nanoporous stamps which have been shown to enable flexographic printing of ultrathin ink features with micron-scale linewidth. Printing with nanoporous stamps requires precise control of stamp-substrate contact force (2-250 mN) and elimination of shear force at the interface among others; these are accomplished using a flexure-supported substrate, and by coordinated rotary-linear motion of the system. We detail the design and evaluation of the P2R machine and demonstrate printing of high-resolution features (<3 mu m line width) with nanopomus stamps at speeds of up to 0.2 m/s.