Why did the Ne'evim run upon feeling fear. Does it pas for a Navi to run from fear. A Navi certainly a complete Ma'amin B'hashem should say Shma when in fear of something! In fact this is what the Gemarah tells us to do! You can't say they were running away from something which is required histadlus because we are told they didn't see anything. If they were in a makom M'tunaf how did Daniel get nevuah there?
We find that even Moshe Rabeinu fled in fear, when his staff turned into a serpent, as the verse says, "... and he fled from before it" (Shemos 4:3).
The reason why Moshe fled was because he sensed the Midah of Din spread against him, and he feared that he might be punished for speaking Lashon ha'Ra (as the Ramban there writes). (Even though fleeing would not help him escape from a decree of Hash-m, nevertheless it is the nature of man to flee when threatened with punishment; see Ramban.)
The same applies to Chananyah, Misha'el, and Azaryah. They sensed an awesome dread, and the knew that the Midas ha'Din had been spread before them, and therefore they fled (perhaps they were confronted with the Midas ha'Din because they did not Daven for the Jewish people, while Daniel, who Davened for the Jewish people, was not threatened with the Midas ha'Din).