It looks like they are beginning to flag accounts for the initial wave of closed beta invites (basically overlapping with the F&F beta). One of my rarely used mules with a kind of weird Windows system profile was flagged.
The following shows up in the region selector (the PTR will also show up here once that is ready to go) above the play button for the Battle.net Desktop app. There was no e-mail sent to that address (so it’s not clear yet if this is still technically F&F or the actual start of closed beta) so those will likely be going out once the beta servers come back online again.

Invites (while limited relative to the player base), will likely being going out in waves in order to stagger the amount of bandwidth used to download the client+content data for those not already in F&F.
For now, accounts are flagged for beta as there is no beta key (thus cannot give them away at this point) – unfortunate since I don’t plan on using the above…