You're right in that flash does have a limited number of write cycles; that limit, as I understand it, is per cell, and not per chip.
There are extra cells in the flash to accommodate failures in individual cells, sort of like spare sectors on an IDE drive. Control circuitry in the flash handles the mapping between memory address and flash cells; it also has a load balancing algorithm to ensure that all cells get roughly the same wear.
When HTC (or anyone else) designs a flash-based device, they take this kind of stuff into account, and specify parts with high enough write cycle limits to last well beyond the expected useful life of the device.