How can I recreate a warm, point-and-shoot film-style flash look with a Canon Rebel T6?

Can I take a short but cynical poke at these?...

They all look like they were done with a fairly close flash - though whether it's on camera or held up by the photographer I couldn't be certain, they seem to me to be predominantly high & camera right, so maybe he's left-handed & held it up at arm's length in his right hand - who knows?
Late edit... a second guess at this is - it's on camera, but the camera is turned to portrait, pushing the flash to the right... makes more sense as an 'easy shot on auto'.

I'm going to go with - it was done entirely on automatic, TTL metering, so the flash & background are both generally adequately lit, though there are annoying hot-spots on light-coloured clothing & some of the subject's faces.
That also, to me, explains how in pic 3 the TTL was badly fooled by how light the sky was against how dark inside the sports ground.

I think then once back in the computer, the Vibrance was dialled up to just below painful. Contrast is pushed as well. White balance is way over towards 'warm'.

I always like to check a photo in CameraRAW to give me a hint as to what may have been done to the exposure/white balance on a photo. It's not perfect, but for something that already feels over-pushed, then seeing what the 'Auto' setting tries to do to recover it can give big hints as to what was done already to 'spoil' it.

This is what it tried to do to one of them - it's not good, it's not meant to be good, it's just a hint as to how far off 'ideal' it is.
CameraRAW window shrunk down to small to get more info in the screenshot.

I honestly wouldn't consider it a 'look' to try to emulate.
The technique has been done a lot better.

You could learn a lot by reading the Strobist