Gauge Description:

There is not a reliable gauge, although this forecast gauge can give some indication of the flow:

Minimum good is probably over 180. 

There was some discussion about estimating the Price by using the Fish Creek gauge, plus the Scofield reservoir outflow.,00060,72020,00010,00095,00300,63680 (Use Firefox, and select Scofield res)
A total of 250 by this method should be a good level for Price Canyon.
200 might be a good minimum.

Another suggestion is White River below Tabbyune Creek, plus the Scofield reservoir outflow, to estimate the Price Canyon flow. 
Zoom in on this map, to see the relevance of this suggestion. It seems to give a lower cfs reading than the first method.
White River below Tabbyune Creek:
On June 1, 2014, only 20 was on the White River gauge, with 120 cfs outflow from Scofield Reservoir, and the Price looked runnable. 

Gauge Information

Name Range Difficulty Updated Level
usgs-09313000 0 - unknown cfs III-IV cfs

gauge graph
RangeWater LevelDifficultyComment
0 - unknown cfs barely runnable-high runnable III-IV gauge is important or has warning

Reports give the public a chance to report on river conditions throughout the country as well as log the history of a river.

When River/Gauge Subject Level Reporter
8y217d22h14m /Price-2. Picnic area above Price Canyon to Castle Gate (Price Canyon) [UT] Price Canyon 0 cfs Thomas O'Keefe