Can I change the flash storage in my iPhone 4? I saw a super deal where I could get an iPhone 4 8GB for such a small amount that I couldn't resist.

Does someone know if it's possible to change the flash storage for a 16GB or 32GB ?

Would iTunes recognize the device and/or enable me to reset it to default iOS and settings ?
No, it is flash memory soldered onto the main circuit board and cannot be changed. It is not similar to devices with removable/upgradeable storage at all. 

In this case "no user-serviceable parts inside" would be pretty close to the truth. iFixit has a great iPhone 4S tear down if you'd like a complete tour of the internals. They have done the same to many devices if you explore a bit, very interesting.