I'm a BC level 2 coach, plus I've done a discipline-specific unit. This is to coach at a youth cycling club both my kids are members of, rather than with a view to using it professionally. Excellent course IMO, and a great platform to build on as a volunteer coach.
In the absence of any other relevant qualification, the Level 3 BC course (which is more performance-focused) is probably where you'd be able to start thinking about making a career in bike coaching, but even with that I think realistically you'd need to augment it with a related area of expertise like physiotherapy or diet/nutrition or even sports psychology.
That said, it appears possible to build up a healthy sports coaching business by putting on a pair of combat pants and taking a bunch of fat women to a park to shove tractor tyres around, so who knows?