Braided or stranded tinned copper for flexible connection?
Two types of braid available: tubular and flat.  Look at wire mfr. datasheet for equivalent AWG or cross section area to determine ampacity.

When you mention flexing, is that primarily in only one axis?  If you need flexibility in two axes then tubular braid might be a better choice.

For single axis bending and torsional bending, flat braid works well.