Was there ever a US 7.62MM Incendiary cartridge?
You betcha. Short lived, it was strictly an experimental developed in 1969 for the USAF for possible use in the 7.62MM Minigun. Cases were standard 7.62MM NATO and bullets were obtained from breakdown of Cal .30 Incendiary cartridges. A smooth seating cannelure was added to the M1 bullet to obtain the correct OAL. Headstamp on most that are seen is LC (+) 69.
API bullets were tested at the same time. It was concluded that both were suitable for Minigun use. I have no idea what ever became of the concept.