Well it's true there is middle class citizens in Thay but always on top are red wizards with no exception. Not even church openly question this, red wizards may have respect for Kossuth but they care little else for other churches (and other religions have no foot hold as even Kossuth church watches for upstarts).
Now, even if you paid 100x times the slave's price, if buyer is thayan red wizard the salesman sells slave to him. Reason? He does not want end up angering a red wizard (and doing so is suicidal). It's possible you get ahead and buy slaves off the market but you unlikely get everything and you may had needed to bribe slave seller to give you chance to buy before red wizards see the stock (until a red wizard realizes what's going on and doubles your bribe price and slave master cannot refuse).
Thay is magoracy dictatorship country, if your not high ranked cleric of Kossuth or red wizard you have no political power there. Despite how rich you can be (as red wizard can simply confiscate your wealth without it being even a crime). Most key thayan trade is based on red wizard created industry of super cheap magic items and slaves. Plus of course occasional spellcasting service rented.
As said, nothing against your concept but you need understand the very climate where your char comes from and understands if red wizard asks you to jump you ask only 'how high?'.
So it sounds like she'd have a hell of a time trying to be a merchant IN Thay, but she could be a merchant in Waterdeep FROM Thay pretty easily. It just means that there's a reason why she left Thay. Maybe she left on bad terms and can't go back without risking her life. Maybe somebody is hunting her. Let's focus on how we can tweak her idea so that it works rather than why it won't work in its present form.
Not a Red Wizard a Thayan of the merchant class your "normal Thayan", who is a Divine Bard (a bard variant that draws magic from a deity using wisdom as the main ability, bards who use arcane magic in Thay have issues a divine power is another matter) and is a Merchant Princess her Guild her faith. And faith is one route to advancement for Thayans of the right stock and not well wizards.
Oh and the Red Wizards may not care about faith but the gods and goddesses are mighty powers that cannot be ignored.
My character likely will invest in two more limited use portals and broker in freeing slaves from Thay, that is for say twice the cost of the slave will buy them and send them to Waterdeep doing work with various interested parties. Its not illegal and should be profitable. And give her a good rep among the locals that matter the good faiths who would pay and the representatives of various races to free some of their people. And she can send goods the other way to profit more. Gates aren't cheap but half the gold should cover two if done right.
Ah! There's a good reason why she may need to be secretive. She wants to remain on good terms with Thayans to keep up appearances and make procuring slaves much easier, but she also wants to free as many slaves as possible.
Here's my idea: Rather than trying to out-right buy slaves, she helps smuggle them out of Thay by way of portals. But smuggling live slaves will royally piss off the owners and the slavers, so she takes a less obvious route - she gives them an herb or potion that makes them appear dead. A dead slave is no good to anyone, and would probably be either used as undead cannon fodder or as gnoll food. In other words, if a few slaves that are presumed to be dead begin disappearing, nobody is going to bat an eye, and as long as she doesn't start smuggling slaves out on a large scale, she can free Thayan slaves without drawing much attention to the fact that their bodies are disappearing.
How does that sound, RubySlippers?