Strictly no, but in practice yes. The contents of the Club Kitchen are BA's property until properly appropriated by a passenger. BA has told J passengers they should help themselves to items they wish to consume during the flight. For everyone else, BA's agents (i.e. the crew) can do what they like with BA's property. So an FA can tell an F passenger it's fine to go get a Mars Bar, or can tell a J passenger its fine to give a Mars Bar to their mate in Y, or tell a kid in Y they can have a Mars Bar or whatever they want.

The only difference is the probability that the FA would be happy for an F passenger to visit the Club Kitchen is presumably 99.9% (if an F passenger said "do you have any Mars Bars" the chances are the delightful crewmember would even fetch the thing). In other cases the probability of success is lower, but it's fine to ask!