Probably in the thousands (or 10s of thousands). It should also have wear leveling which means that you would actually have to write the entire 1GB NAND 10s of thousands of times to 'wear it out'. 10,000 writes would mean writing 10TB to the NAND memory, accounting for wear leveling. There is not a specific limit, it will just start to have corrupted data. There is also some unused (spare, if you will) memory that can be used to replace bad spots as they come up.
Remember, everytime you download an app, or anything that writes to the /data directory, you are writing to the NAND memory.
Long story short, I highly doubt you will ever start to wear out the NAND memory of the phone. If the average ROM is 130MB, 10TB / 130 MB = 77,000 ROM flashes.
Sent from my SPH-D700 using XDA