On PS4 I received the task to win a battle using the Khetar banner. I changed my banner on my team as suggested and invaded in pvp. I won but the task did not complete. I then tried to set Khetar as my home kingdom on top of equipping the banner. I again played a pvp game and won without the task completing.
I will try again using quests and challenges to see if the task completes with them. I will update as soon as I test the other battle types.