I made a weapon in D&D 5e: A silver-plated scimitar that has a +2 wand of the war mage fused along the back of the blade, and an Arcane Focus crystal embedded in the hilt.
I also placed a continual flame evocation spell on the crossguard, making it appear as if flames danced on the crossguard. It acts as a torch in terms of utility but does not need oxygen and does not burn anything.
What rarity should it be? Common, Uncommon, Rare, Very Rare, or legendary?
The primary actor in this item is the Wand itself, which as you've linked is a Rare item due to the +2 modifiers.
While the other parts add some utility, there really isn't anything that's going to push the rarity up another level.
The silvered scimitar makes this wand a weapon as well. While that improves the utility of it, I don't think it's a real issue. The scimitar doesn't benefit from the +2 because the Wand is specific in how it works, so the only real benefit here is the melee option and the silvered property. On the flipside, it's now part metal and someone casting heat metal on it would be a problem for you
The arcane focus covers your bases to make sure it's an arcane focus, but again, that's not a big deal.
Finally, the continual flame is a neat touch, but doesn't offer anything that's going to upgrade it's rarity. In fact, it may create more problems than it will solve. You've got a continuous undousable light source on your weapon now. Fighting in dark environments where stealth is key may create a problem for you and your party.
