Actually it makes sense to use it as a flag: it looks good!

Also, the symbol of a important leader is usually a flag used by it's people, and Lúthien lived between the Nandor after her and Beren returned from the dead, so a flag with a flower and the Silmaril would fit perfectly for them.
The heraldries of the men could be turned 45° to be countries/peoples flags (as Finwë's was also the flag for all the Noldor, just turned this way). For the Noldor, I had originally used the heraldries of Fëanor, Fingolfin and Finarfin for the 3 houses, but there are other options. For example, Finwë's (for House of Fingolfin), the Silmarili's (for House of Fëanor), and Finrod's (for House of Finarfin).