For some reason the game isn't reading your VIP status properly (most likely).
You could try logging off then back on to see if it refreshes your status.
Also, you FULLY completed any previous Ouro flashbacks or AE missions and are no longer in a TF mode right?
Clicking on the linked image above will take you off the City of Heroes site. However, the guides will be linked back here.
Thanks, no luck though. 
First things first.
Are you level 50?
Is your Alpha Slot completely unlocked? Not partially unlocked, fully unlocked.
Have you run the DA arcs normally (not through Ouroboros) first? You have to start with the introductory contact's mission (Captain Nolan in Peregrine Island for heroes, a threatening Arachnos message for villains). That will get the DA arcs started on your character.
You will have to complete the Heather Townshend arc in this manner (running it through the DA contact chain) before you can run it through Ouroboros. Also, I recommend doing the personal missions during the initial run through of the arc as it seems to be counting the arc as still open if you don't so these (even though they are supposed to be optional). The same applies to all of the DA arc missions. You must do them as part of the DA chain normally before doing them through Ouroboros.
If you have met all of the above conditions and it still isn't letting you access it through Ouro you will need to file a /petition in-game or file a support ticket using the Ask A Question tab or the Live Help tab (if it's during hours that it is available) at the CoH Support site.
If the game spit out 20 dollar bills people would complain that they weren't sequentially numbered. If they were sequentially numbered people would complain that they weren't random enough.
Black Pebble is my new hero.
No, I haven't run the arcs yet normally. Is that necessary for other Flashbacks now, or just this one?
I also haven't slotted my Alpha yet. Again, is that something this Flashback requires that others do not?
Thanks for the help.
It's only necessary to run them normally first for the DA arcs as far as I'm aware.
You don't have to have Alpha slotted, only unlocked fully in order to run the DA arcs as your own mission.
EDIT: I'd also recommend talking to Taskmaster Gabriel as soon as you start the DA chain and then once you finish all of the DA missions. He gives a reward of 2 Empyrean's for completing all of the DA arcs, whether it is on the initial run through or on subsequent runs through Ouroboros. You can get this reward once per week. Also, if you do the side missions for Max's arc (either through the first run or through Ouro) then running the final mission subsequently will remember that you have run them and you'll have the helpers. It isn't necessary to run the side missions each time after you've run them once. I think this is part of the reason Max's arc doesn't have a reward table at the end.
If the game spit out 20 dollar bills people would complain that they weren't sequentially numbered. If they were sequentially numbered people would complain that they weren't random enough.
Black Pebble is my new hero.
Is there a trick to accessing her through Ouroboros? When I click on her from the Pillar list, it says I must be a VIP and not on a team (both conditions met).