Yes, they can! With a Flesh Bound demon, or in this case MC, the only limit is the imagination.
I suppose a Flesh Bound could create a human weapon - be it something either fantasy, like a sword, or modern, like a gun - from their own ‘flesh’. In the case of a gun, the MC might not need to know how a gun works in order to get it ‘fire’, but this might be bordering too closely to DMC’s infinite ammo mechanic.
Alternatively, the MC’s flesh gun could resemble something like this with the ‘bullets’ being actual shards of bone from the MC’s body.