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.