If it is truly a freewheel hub (freewheel spins onto threaded hub), then you will need to remove the old freewheel (you'll need a specific tool), spin on a single-speed freewheel, and redish the wheel. If it is a cassette hub (splined cogs with a lockring), then the conversion kit should work. As for the cranks, how flat is Lincoln? 52 might be a little steep, but you'll have to figure out what works for you where you live. I live in a city that is mostly flat, with several hills and valleys. 46/18 works for me on my fixed cross bike. YMMV.
Oh, search Sheldon Brown's site for "Single Speed Conversion", the man knows everything.