The Gundam vs. Hello Kitty Line account can be found here, and their battle is set to continue until the end of the year.
To sign up for Team Gundam or Team Kitty, first befriend the Gundam vs. Hello Kitty official Line messaging app account, then select which side you want to join.
The participating merchants will change monthly, with the first batch set to be udon noodle chain Marugame Seimen and grocery/department store Itoyokado.