An official Splatoon 2 headset is on the way as part of a partnership between Hori & Nintendo. The headset can be used for voice chat in-game and is even an actual accessory Inklings can wear.
We also get our first look at how voice chat will work on Nintendo Switch via this diagram:
By plugging the headset into the dongle, you can then plug the microphone into your phone and the speakers into your Nintendo Switch. Information on how exactly Nintendo Switch Online is planned to work can be found here.
Splatoon 2 launches for Nintendo Switch on July 21st, 2017.