Can I change the flash storage in my iPhone 4?
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.