Is there an upper bound to the amount of rain that can fall in an hour?
From http://www.srh.noaa.gov/eax/?n=holtmorecrain1947

A very moist airmass was in place across Missouri during the afternoon and evening of 22 June 1947, as evident by dewpoint temperatures in the middle 70s across Missouri during the afternoon hours
Advances in meteorological science led Locatelli to speculate that the thunderstorm that produced the historic rainfall of 22 June 1947, did not develop along a classic surface cold front, but to the east of a surface dryline (drytrough) and underneath a cold front aloft that had origins in the Mexican plateau.  Regardless of the causative surface and upper air features, a complex of storms at a scale not measured well in the data-spare period of the 1940s developed near Kansas City and moved across Holt, Missouri, depositing 12 inches of rain in less than one hour.  Rain continued to fall on Holt after the 12 inch deluge for the next couple hours, but only amounted to an additional one-half inch.

A rare meteorological event occurred that day.  I offer a semi-empirical frame of reference that takes  into account that the most extreme rainfall rates occur for a short duration (e.g. a few minutes).
In &quot;A methodology to classify extreme rainfall events in the western mediterranean area&quot; by Casas et al., (2004):
http://link.springer.com/article/10.1007%2Fs00704-003-0003-x
they show rain rates of up to 0.5 cm/min sustained for several minutes (based on a large network of rain monitors in Barcelona).   IF that could somehow be sustained for an hour, that would give a rate of 30 cm/hr (which is what Holt saw).
For comparison, the most extreme rainfall rate measured in one minute in the USA is 3.1 cm (1.2 in; see http://wmo.asu.edu/world-greatest-one-minute-rainfall ). Actual rain doesn't continue at such an extreme rate for much longer, but would equate to 186 cm per hour (6 times what Holt, Missouri saw in 1946).  The link that kwinkunks provides http://www.bom.gov.au/water/designRainfalls/rainfallEvents/worldRecRainfall.shtml shows a world rate record of 3.8 cm/min which, if sustained, would equate to 228 cm per hour.