Sadly you have few options.
The shutter is not supplied as a separate part by FLIR so you would need to strike lucky with the service tech at a service centre to obtain a salvaged part from a faulty Lepton. The Lepton is pretty reliable as a core so you do not see faulty ones for sale that you could rob the shutter from. Your easiest, though not cheap, option, is to buy one of the faulty FLIR One G2 units that appear on eBay and either transplant the whole lepton core (recommended) or just its shutter (easily damaged) You are looking at between £50 and £100 for a used faulty FLIR One G2, depending upon the market and condition.
Sorry it is not better news. I have plenty of spares donor FLIR One G2 cameras containing the Lepton cores but all those cores are working so need their shutter.
Fraser
UK