Can I be retroactively promoted to E-5 if I was flagged for an investigation that came back with no findings?

A enlisted promotion that was wrongly denied due to an erroneous flag has a remedy for correction in the regulation.
However, in your case the flag was valid, regardless of the investigation outcome,,the flag was allowable and correctly emplaced, then lifted when no longer required.

Your situation is not spelled out in the regulation that I can find, so it would take an appeal to HRC, stating the facts, dates, results, and if you can, a letter from a senior commander that endorses your position you would have been promoted had it not been for a false allegation and ensuing investigation.
I dont expect an answer,,,,, but just to put it out there, a investigation result that recommends no charges is not the same always as not guilty. And the human at HRC is going to think that as well.... If a commander thinks you are not guilty of what ever the charge was they will likley provide that letter refrenced above...and that would help the HRC person making a grey area judgment call do so with a clear mind.

Likewise, no letter of endorsement and a judgment call that can go either way, will likley result in a NO. The way I read the regulation I think your looking at a NO and good luck next month. You were under investigation and the flag was valid....and that means you were not eligible for promotion.

Had the reason for the flag been erroneous (mistakenly marked AWOL, Over body fat, pending UCMJ) then the flag would have been erroneous as well, and you would have a case.

Stand by Board?

I would highly recommend that you run this up your chain of command. IF you in fact were eligible, recommended, and the fact that you were under investigation that precluded you from being promoted, I would suspect that yes, you may be able to be promoted and backdated. I would also ask to see what regulation prohibits this process. Semper Fi.