You can calculate the miles for example on this site: http://gc.kls2.com/

I didn't check valid flights, but you have to remember that the open segments are calculated in the miels for your total itinerary. This means that your itinerary isn't ams/lhr-lim,lpb-scl-pmc,ush-scl-ipc,ipc-ppt,ppt-syd,syd-bkk,hkg-pek,pek-ams/lhr but rather ams/lhr-lim-lpb-scl-pmc-ush-scl-ipc-ppt-syd-bkk-hkg-pek-ams/lhr (in term of miles).

No OW flight between LHR-LIM, so it would have to be LHR-MAD-LIM. I din't check LIM-LPB-SCL availabilty on OW (or LA).