Fly to Frankfurt on DE with miles, book second flight either on AZ or LH to Palermo.

Fly to Dublin on EI with miles, book second flight on Ryan Air to Palermo.

Fly to LHR on BA with miles, spend the night, fly to Palermo on either Easy Jet, Ryan Air, or BA from one of the many London airports.

Bonus Creative Option: Fly FI through KEF to MXP, take the train to Genoa, take the ferry from Genoa to Palermo.