Playing Keynote on Smart tv

I believe with the JPEG export you're already doing it the best way. You could try exporting a movie, but it will depend on the TV as to whether it can play it—and you'll have less control, i.e. it will advance to the next slide on a timer, though you could always pause the movie. You could instead:

• Connect your computer to the TV with an HDMI cable (you might need an adapter)
• If you have an Apple TV, mirror your computer to it (similarly you can do this with the Google Chromecast)