It‘s a double entendre, so two meanings at once.
"Flight" as to flee
As user067351 says, the statement is borrowing a term-of-art (insider jargon) from the financial industry:
A flight-to-quality, or flight-to-safety, is a financial market phenomenon occurring when investors sell what they perceive to be higher-risk investments and purchase safer investments, such as US treasuries or gold. (Wikipedia)
The literal expression means fleeing high-growth but high-risk investments due to an expected downturn in which the risk will exceed the growth, so selling them high and moving into safer investments like bonds.
The speaker is saying that US MBA programs are the best, and despite improvement in foreign school programs, foreign students still feel safer investing their time and tuition in the best.
"Flight" as desirable transportation mode, esp. across seas
And "quality" as the speaker's own institution :)
The metaphor is that the foreign students are "flying" (to cross the ocean) to a "quality" university.
This is why the speaker selected "flight to quality" instead of "flight to safety" above. The latter make it sound like they are refugees, whereas the former allows the speaker to brag.