As what they're afraid of is not specified, I would say "They have no reason to be afraid." instead of "They have no reason to fear."
Using fear intransitively seemed a bit unusual to me, but you're right, it's fine.
Can you translate "proč" in general as "reason"? The only translation I can find for "proč" is "why".
In this specific usage it is the most straightforward translation. It is very similar to "Nemají důvod se bát." where důvod=reason. You cannot always just pick dictionary equivalents of each word when translating sentences.
I think that "They have nothing to fear": should also be accepted as correct.
This may or may not be helpful to you, and it's sort of a head game. But if you think about the literal translation as "They do not have WHY to fear," it can be easily turned into "They have NO REASON to fear."