I've been doing this for awhile however i noticed Blizzard hotfixed the window of time you have to apply Eternal Flame to the player and i've got it working again. I'm only posting this because i feel like they're going to fix it eventually since the amount of time you've been allowed to put Eternal Flame up has been changed a few times, so have fun while it still works.
To start off you have to be a paladin speced for Eternal Flame
Enter the Arena
Get your holy power up to 3+
When the timer (countdown till the arena starts) on your screen is JUST about to change to 1, so during the transition between 2 to 1, you cast Eternal Flame on the target, and it will not get taken off the target. If you have the HoT on the player anytime before 2 seconds, it will remove the HoT and anytime after the 1 it will remove your holy power, so you need to be fast.
You may also put them on pets so this way half of what it heals the pet heals your beaconed target as well, i'm not sure what the time frame is for putting it on pets however i usually do it around 5 seconds.
How is this an exploit? You get to have a 30 second HoT on someone which otherwise you arn't suppose to have coming out of the starting gate. This is extremely helpful if you play with a feral or rogue as you can put it on them b4 the game starts and they'll have a HoT up.
Cheers.