How can I destroy the flag without falling to my death?

I've never had much problem. I have various methods of climbing ships.

Usually if I have to capture a flag my tactics are after boarding starts

  1. Use the swivel gun to do what damage I can.
  2. Use the quick elevator thing on my own ship to get up to the platform.
  3. Shoot enemy soldiers on the central platform (or others).
  4. Swing across to their boat on a rope and assassinate people and then fight generally til I am at or close to the soldier death limit (if one or two short I hope that my crew will finish the job).
  5. Use the quick elevator on their ship to start my ascent. There is of course no soldiers up there any more.

This has never really failed me. I do occasionally skip some steps but the above is, in my view, pretty efficient and pretty foolproof.