This idea has an immediate appeal to those of us who appreciate symmetry. However, I strongly suspect this would be an extremely impractical flag to add...
See, closing and re-opening aren't exactly equal. Most notably, closing requires you to specify a reason - reopening does not. This cuts both ways: closing requires more effort, but other voters also have a reason they can either agree or disagree with; unless the person voting to re-open left a comment, there's nothing to indicate why he thought re-opening was a good idea. Hopefully it's obvious... But if not, a good many voters won't do anything to change the status quo.
It's already possible to flag for re-opening, of course. And over the years, over 900 flags have been raised on Stack Overflow for this purpose with 37% resulting in the flagged questions being re-opened. That's actually quite good - the chance of getting a question re-opened via the reopen queue is somewhat less. Part of this higher success rate is almost certainly due to the ability of moderators to reopen anything with a single click - but still, you have to convince them to do so. And this is where the current flags have the advantage over a predefined "please reopen" flag: they give folks an opportunity to explain why the question should be reopened.
To be clear: I'm not totally against this idea; I like that it would increase the amount of community review for closed questions without creating more work for moderators. However, I think there are more effective ways to do that which have less potential for just generating noise in the queue. For example:
Adding items to the queue in response to 3rd-party edits. Currently, this is done when the author edits, but not if someone else does the same. It would be possible to change that - although there are some pitfalls we'd have to avoid.
Adding closed but answered items to the queue if/when an answer collects an up-vote. If someone understood the question well enough to answer it, there's at least a small chance that it's salvageable; reviewing these questions as a matter of course could also prioritize those questions that've already attracted some amount of effort from others and thus are more "deserving" of preservation.
Adding popular items to the queue immediately upon closure. Let's face it: the reason most questions that get 1 reopen vote don't get reopened is because they are not very good questions; that's why they got closed in the first place. However, there are a comparatively small number of decent questions that are simply a poor fit for Stack Exchange in general, or were asked in a way that rubs a few people the wrong way - these tend to be the ones that folks fret over when discussing closed questions, since some of them could be salvaged with careful editing.
Something else I haven't thought of yet...
Failing all of that, it might be worth adding a re-open flag that prompts for a reason and then displays this in the review queue - but frankly, this seems like a lot of work for a very small chance of success.
Update: declining this, since pretty much everything I suggested has been implemented as described here.