Etymology:
Unlike magnetic media in which a magnetic head is used to flip tiny bits of ferro-magnetic molecules on the disk, in the old days, chips like this would be EPROMs that had a little circular window on the top of the chip, through which specialized equipment would literally flash a beam of ultra-violet light to erase the chip, allowing it be re-programmed (somewhat like how CPUs were manufactured with beams of light baking the transistor masks into the silicon wafers). Think of erasable CDs or DVDs; to erase them, the laser basically “melts” (not technically) the material, then it can be written.
(Note, just like leaving CDs/DVDs in the sun can damage them, leaving an EPROM exposed to the sun could also damage them, so they often had protective stickers covering the flashing window.)
These optically programmed EPROMs were too expensive to manufacture for general use, so EPROMs were often made without the window, thus making them write-once and non-updateable. As a result, they were later replaced with EEPROM (Electronically-Erasable, Programmable Read-Only Memory) chips, making them much easier and cost-effective since they could be updated with the customer’s system itself instead of needing to be sent to a shop to use the special equipment.
That’s where the term flashing comes from, and like most outdated terms, it just kind of stuck.