You "can" get through Rainbow via Kane Springs Road to Caliente. I say "can" as it's passable, yet technically closed to through, non local traffic on the asphalted section. There was a real heated debate over who owned the asphalt road into Caliente (has very large, Jeep swallowing sections gone from the floods) but I hear the state is supposed to fix it since the Bradshaw family turned the Elgin "one-room schoolhouse" over to state parks, as an addition to Kershaw-Ryan Park. Haven't got a confirmation on that yet though.
The "old way" was from Moapa to Elgin along the tracks, and up the asphalt road from Elgin or even by continuing to hug the tracks. Like famgeo says, the UP has been closing off sections all through Rainbow, Kane, and Clover Creek Canyons. I've run into many a locked gate recently. Sucks really, as the whole trip was quite interesting, and I've always wanted to run the rail to Utah from Moapa.
Depending on where you leave Vegas from, it's about 150 miles to Caliente by highway. The Kane-Elgin cut off cuts something like 35 miles off. IIRC it's around 65 miles to the cut off, then 38 miles of gravel to Elgin, then 11 asphalt/gravel/bigfreakinghole! miles to Caliente.
There are numerous rock art sites in Rainbow Canyon, and their location is listed in the Lincoln County site.
http://www.lincolncountynevada.com/index.html