What's the most flexible type of screw, ie one that won't break when
bent? Steel and brass doesn't seem that flexible.

I have an application that needs a screw that won't sheer if bent more
than 20 degrees (the application is a bit complex to go into here!).

A thought - are there screws made from thick wire (5mm or so), as is
the case with wire nails? That would be ideal as wire nails are nice
and flexible.

Thanks