The Vimanas of the ancient Sanskrit epics and Hindu texts are flying cars.
They are distinct from the horse drawn Vedas
They are described in the Ramayana which the earliest complete version can be dated to the 11th century CE (though fragments are dated as early as 6th century CE).
From the Ramayana:
"The Pushpaka Vimana that resembles the Sun and belongs to my brother was brought by the powerful Ravana; that aerial and excellent Vimana going everywhere at will ... that chariot resembling a bright cloud in the sky ... and the King [Rama] got in, and the excellent chariot at the command of the Raghira, rose up into the higher atmosphere.'"
It is the first flying vimana mentioned in existing Hindu mythology texts (as distinct from the gods' flying horse-drawn chariots).
There has, of course, been much speculation about their meaning. I admit this answer is a bit out of the box and doesn't demand a mechanically motorized car. But it certainly is the oldest possible description I know of.