In the wording of the Flock of Familiars spell (Lost Laboratory of Kwalish, p. 57), we find:
You temporarily summon three familiars – spirits that take animal forms of your choice. Each familiar uses the same rules and options for a familiar conjured by the find familiar spell. All the familiars conjured by this spell must be the same type of creature (celestials, fey, or fiends; your choice). If you already have a familiar conjured by the find familiar spell or similar means, then one fewer familiars are conjured by this spell.
Meanwhile, in the Find Familiar spell, we're given:
As an action, you can temporarily dismiss your familiar. It disappears into a pocket dimension where it awaits your summons. Alternatively, you can dismiss it forever. As an action while it is temporarily dismissed, you can cause it to reappear in any unoccupied space within 30 feet of you.
Of interest, conjure is synonymous to summon, which is antonymous to dismiss.
If I were to temporarily dismiss my familiar from Find Familiar and cast Flock of Familiars at level 2, would I expect to summon three new familiars, since the original is no longer conjured? Could my initial familiar then be re-summoned back on top of those already present, making a total of four?
Granted, I only know the part of the spell from Lost Laboratory of Kwalish that you posted, not owning the book or having read it, but I think it's enough.
It specifies that
If you have a regular familiar by the Find Familiar spell, it has still been conjured, even if it exists in a pocket dimension. It will remain conjured until it is dispelled or killed.
My proof for this is that the same wording exists in the official Find Familiar spell.
Here we see that you can only have 1 familiar at a time (per this spell) - and even if it has been dismissed into a pocket dimension, casting the spell again would not create a new familiar - only change the form of the one that has been dismissed.