It sounds like you bought a foreclosure or possibly short sale. A "flip tax" is a private transfer fee. It is considered a restrictive covenant. Certain lenders will not lend in buildings with restrictive covenants. That is why FHA does not loan in any coops. "Board approval" is also a restrictive covenant. Even most Manhattan condos have a restrictive covenant "right of first refusal" many lenders do not want to loan on properties with restrictive covenants.
In fact, if it wasn't for REBNY (real estate board of NY) lobbying efforts no FHFA (Fannie Mae) lender would loan in any building with a flip tax.
In HDFC buildings the amount of "flip tax" is usually based on profit. If there is such a high profit it doesn't make sense that it ended up owned by bank. The coop has the first lien and in a coop only the board can initiate as foreclosure. Although a "flip tax" is usually the burden of seller in a foreclosure or short sale, the buyer is getting a great deal they usually need to come up with additional cash at the closing. In NY the onus is on the buyer to do do diligence before signing a contract.
I hope you had a NYC coop attorney advice you of possible risks before you signed a contract on a bank owned property in an HDFC coop.
Not some Bank?
In either case; you probably can't sue them:
I am not a Lawyer, and I do not dispense legal advice,
But I believe that in order to sue somebody, you need to show a LOSS.
Being deprived of the house, is not a loss.
You have not suffered a financial loss; have you?