Your assumptions are faulty.
You're making a lot of unsupported assumptions by claiming it's a given that "find familiar can produce 27.5 gp more in sales of Sprite equipment than its own cost."
First, I'm not sure where you even got 27.5 from. On selling equipment, the Player's Handbook (p.144) says:
As a general rule, undamaged weapons, armor, and other equipment fetch half their cost when sold at market. Weapons and armor used by monsters are rarely in good enough condition to sell.
Assuming you have a full sized, undamaged longsword (15 gp), shortbow (25 gp), and leather armor (10 gp), you can generally sell those for half price, which adds up to only 25 gp, and that's before considering the component price (10 gp) of casting find familiar. And that's only the "general rule"; it's up to the DM to decide whether you can sell any given piece of gear at all and for what price.
Second, is a sprite familiar considered a monster, and thus "rarely" bears items that are worth any sale value? Most likely the answer is "yes", though this is really up to the DM to decide. Note that quality isn't the only consideration here; the sheer size of the items can itself be a reason to say the items aren't worth their potential sale value. That really leads into a separate assumption you're making--
Third, is tiny equipment worth the same price as the usual stuff in the first place? I would think it's obvious that it isn't. Even if a tiny faerie creature might be able to use it as a longsword, it's obviously nothing more than a belt-knife to a human, if even that. The DM will have to decide what the base price of the equipment is when it's not the "expected" stuff from the equipment table. This can go the other way, as well -- a giant's greataxe may not be worth much at market because it's essentially worthless to a human except as a curiosity or scrap metal.
Fourth, while the Sage Advice article says a familiar drops anything it's carrying "when you dismiss it to its pocket dimension", it is silent on the question of whether ending your association with the familiar by permanently dismissing it causes the gear to vanish or remain. The game is similarly silent on what happens to gear dropped by other summoned beings, such as by conjure celestial or conjure fey. Your DM will have to decide whether you can conjure an angel, disarm it, and then dismiss it so you can keep its holy sword.
As a side note, my interpretation of the Sage Advice answer is that it was meant to prevent you from using a familiar as an extradimensional storage unit or a way to teleport items from wherever the familiar is to a location within 30 feet of you, and the 'drop everything' effect should not be interpreted to apply to the equipment that's actually in the sprite's stat block. (I have other issues with that particular Sage Advice, though. I'd personally be a bit annoyed if I had my familiar attune to a magic item, only to find I now have to constantly go collect it every time my familiar pops into its pocket dimension. I don't believe that was the intent of the ruling, and that it was an ill-considered way to patch an exploit, but that's a whole other discussion.)
If you can do that, then in theory you could do the same with a familiar.
You might notice a theme here. It's up to the DM to decide. This isn't even a valid thought experiment, because the question depends entirely on having a DM that will go along with a frankly ridiculous "loophole" in the rules that is no such thing because virtually every step is based on "usually" and "generally" that obviously wouldn't apply to sprite-sized gear that may or may not vanish into the fey realms when you release their owner.
What about Flock of Familiars?
Okay, so let's leave aside the question of money and just focus on the spell in question. Can you summon Sprites with a flock of familiars spell in the first place? I would say no, you can't.
The Warlock's Pact of the Chain says:
You learn the find familiar spell[...] When you cast the spell, you can choose one of the normal forms for your familiar or one of the following special forms [...]
Flock of familiars says:
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.
I can see how you could interpret these two as combining, but in my opinion, they don't. The special forms are accessible only when you cast find familiar in specific, not any other spell or ability that allows you to summon familiars. The flock of familiars references back to the find familiar spell for the sake of brevity, not to allow you to summon more powerful allies if you have the right combination of powers. And in any case it specifies that your familiar flock have animal forms, which excludes sprites.
And finally, if you could summon sprites with flock of familiars and they dropped their gear, would it remain when the spell ends?
Well, that's back to the "What about an angel?" question. Summoning spells in general don't specify what happens to dropped or lost equipment when the spell ends, but presumably the intent is that the equipment a spirit brings with it into this world is only as material as the spell makes it, and when the summoning spell ends, so does the material reality of its stuff.