If we're using the fast setting quikrete for poles for a chainlink fence and it's supposed to rain heavy that night, will it mess up the concrete?

I would wait. Not sure if it is necessary, and sometimes it is good to keep concrete damp while it cures, but you say "heavy" rain, so I'd put it off for a day or so.

The time after which rain will affect the concrete depends upon the severity and duration of the rain, and to some degree, whether you mixed the QUIKRETE® Fast Setting Concrete Mix with water before placement. A light rainfall after the concrete is reasonably hard set after several hours can actually contribute towards the successful curing of the concrete, whereas a very heavy downpour earlier on can have an impact on the strength and surface quality of the concrete, particularly if it is troweled excessively during or after the rain. Please contact the QUIKRETE® Technical Center directly at 1-800-282-5828 if you would like to discuss further.