Flexible substrates are not a problem - the industrial solution is polyimide (Kapton) or just really thin FR4. The problem is inflexible components. As soon as you bend a curved surface attached to a small flat rectangle (IC), it pulls at the joins.
You might get better results with bare die+wirebonding, then encapsulating with slightly flexible epoxy. That would allow the bondwires to flex and take up the bending. Doesn't help with the discrete components or the battery.