I came across some hard to reach nuts and bolts on my car today, it took me really long to get them out. I am wondering if it is possible to use a flexible shaft for such things. The question is how much torque they can transmit without being damaged or broken. The bolts today were torqued with about 30Nm (~22 lb ft). Do you think it would be possible to attach a flexible shaft to a cordless screwdriver and get such bolts out?
In theory, angled joints transmit all torque. In practice however, the larger the angle the more loss of torque.
The sort of flexible shaft in your image will not transmit enough torque to loosen a bolt tightened at 30Nm. It's meant for screwdriver applications, and even there it's mostly a gimmick.
If you're unable to use a combination of normal extensions, you might want to use something called a "wobble extension", which allows a relatively small angle. You can also try using a universal-joint adapter, which allows a somewhat larger angle.
If you still can't reach the bolt you need to reach, you'll need to remove parts until you can reach it.