Generally no.
If the adorn flintlock is somehow lost or destroyed …. it’s gone. You can purchase additional flintlocks but they are not adorned. The adorned Flintlocks are given out by the Monks of Altheres are essentially unique to them.
Theoretically you could somehow potion the Monks for another one. I could potentially see a hero getting another flintlock from the Monks if the First was valiantly lost defending Altheria or prominent Altherians. In a home campaign that’s something you’d need to talk to your GM about. In the living campaign you’d need a special event or help from a person on the campaign staff