Yes you can play each this way:
Chrono Trigger DS:
Dragon Quest III, Nintendo Switch eShop, also on iPhone and SNES emulator is pirating is fine with you. The Recommended choice is the Nintendo Switch version on eShop here, its the closest official version out on the Nintendo eShop right now for you to buy, and its very cheap only $13. Check it out here:
https://www.nintendo.com/en_US/games/detail/dragon-quest-3-the-seeds-of-salvation-switch/
Final Fantasy VI on the SNES Classic, you can buy it here. On the system it will be titled Final Fantasy III because Squaresoft changed the name back then in order of localization release, FF I was fine, FF II US is FF IV really, FF III US is FF VI really, you get it?: