Can anyone suggest what this "click/clack" noise coming from my BB might be a result of? It's a Wheels Mfg eccentric, PF30. The bike is newly assembled.
If the clicking is happening during the power stroke of the pedalling, it is most likely bearing related.
You need to figure out if the chain/chain tensioner/drivetrain is involved or if it is the bearings. two quick checks would be:
Check chain tension throughout the pedal stroke to ensure it isn't overly tight at a particular point. Rotate the pedals very slowly and check the tension by deflecting the chain vertically. A safe starting point is about a 1/2" of movement. if the chain gets significantly tighter at a certain point, the chainring is not concentric, see chain tension below.
With the bike on the ground, stand next to it drive side, put the drive side pedal at the bottom of the pedal stroke and push it downward towards the ground while holding the bike against the force (by the seat and/or handlebars). this should deflect the bottom bracket out of line from the axis of the bike (similar to when you apply power to the pedals). As @criggie mentioned below, it would be a good idea to remove the chain from the chainring before doing this. While it's off, rotate the cranks and push side to side to ensure they spin smoothly and don't have any play. Any clicking or resistance here should be from the bearings/bottom bracket adapter, see bottom bracket clicking below
It could be that the chainring isn't perfectly concentric on the spider. if the chain was tensioned at a slacker portion of the pedal stroke, the tension on the chain would be too high in the other portions. (Assuming there is no chain tensioner involved) This could cause a lot of force pulling on the chainring/bottom bracket and force one of them to click or creak.
Ideally, a singlespeed should have a frame with horizontal dropouts or track-style horizontal fork ends. With this type of frame, the chain tension is regulated by moving the rear axle back and forth in the fork ends. If the chain is too tight, the drive train will bind, perhaps only at one angle of the pedals (chainwheels are not usually perfectly concentric). It should be tight as it can be without binding. If the chain is too loose, it can fall off, usually at the most inconvenient possible time.
Set the rear axle so that the chain pulls taut at the tightest part of the cranks' rotation. One at a time, loosen up each of the stack bolts, and tighten it back just finger tight. Spin the crank slowly and watch for the chain to get to its tightest point. Strike the taut chain lightly with a convenient tool to make the chainring move a bit on its spider. Then rotate the crank some more, finding the new tightest spot, and repeat as necessary.
This takes a little bit of your hands' learning how hard to hit the chain, and how loose to set the stack bolts, but it is really quite easy to learn.
Tighten up the stack bolts a bit and re-check. Tighten the stack bolts in a regular pattern, like the lug nuts on a car wheel. I start by tightening the bolt opposite the crank, then move clockwise 2 bolts (144 degrees), tighten that one, clockwise 2 more, and so on. Never tighten two neighboring bolts in a row. You may prefer to go counterclockwise, but try to get in the habit of always starting at the same place and always going the same way. This reduces the chances of accidentally missing a bolt
Bottom Bracket Clicking
Ensure that all threads and contact points are greased appropriately. Ensure they are all tightened to the proper torque - bearing preload on the cranks (non drive side cap and pinch bolts if pplicable), bearings in the eccentric adapter, adapter in the frame. If the clicking continues, slightly tighter is probably OK.
Bottom Bracket Installation
Another possibility I just thought of is that the bottom bracket was installed with the proper spacer configuration. I believe for Shimano on a 68mm shell there should be 3x2.5mm spacers which get installed 2 on drive side, 1 non drive. Without all the spacers there would be a significant amount of play and it's unlikely you would have made it this far, but I felt it was worth mentioning for completeness.