Sorry to say to repair this will require a new logic board. You just can't replace the flash chip due to how the logic board is designed (SMT). And it will be costly! Not really economical to repair.
If you tried desoldering the chip you will likely disturb or damage other components as they are so tightly packed. While not quite the same layout you can review Step 13 in the iPad2 teardown to get an idea on how things are laid out iPad 2 Teardown. Frankly I haven't seen this flash chip available as a replacement chip from anyone (you can buy sticks of a 1000 units from the manufacture). Which makes even the thought pointless.
The error condition is clearly a flash cell failure that can't be remapped by the onboard controller to a different cell (likely all of the spare cells have been used). This is a part defect nothing you could have done in the short time you had your iPad that could explain this.
You really need to contact Apple (up the food-chain) to get this fixed. Don't take no as the answer here from the front line people speak with the the service manager at the Apple Store then the store manager and if that doesn't work press them to speak with someone higher.
Make sure you have as clean a system (no dirt buildup) and if you don't have one get a case with a cover lid. Also make copies of your receipt of purchase of your iPad or your bank statement (if you don't have the original receipt). Black out your bank account info and other charges and what you have in your account (You don't need to tell them how rich or poor you are). If you used a credit card same thing, but I would give them the last four digits of your card.
Also check with your local government on what your laws are for warrantee coverage. In some countries they have longer periods of mandatory coverage.