Clicking in just one chainring I wonder if anyone can suggest any reason why I might be getting a regular clicking (two to each crank revolution, at the same place each time) from the crank/BB area of my bike. I understand these things can be difficult to diagnose, but just hoping I can be guided down the most likely paths.

I recently took the bike to a shop and they said the only thing they could do was replace the free wheel, which I found odd as the sound is unmistakably coming from the front end of the drive train. I can't spot anything visually wrong as I turn the crank, but the clicking only happens in the second chainring, not the first or third. I've had a good look at this chainring and it doesn't look excessively worn, although there is the odd tooth that is clearly much more pointed that the rest, to the point of resembling knives. Also the chain runs clear of the front derailleur, so I'm guessing that can't play a part in this.

Could it be that the chainring just needs replacing? Any other suggestions gratefully received! Thanks.
Inspect the teeth of the chainring for damage. A single one might be damaged from hitting some obstacle. It may then produce a click when taking up the chain at the top and again as it drops the chain at the bottom of the turn.

The best way to do this would be to suspend the bike and have the chainrings at eye-level. Don't turn the bike upside down because it could change the conditions under which the clicking appears. Also try out whether the clicking appears when the crank is turned backwards.

Good luck and patience because sources of noises are notoriously hard to spot.