You can't do this directly with DungeonBuddy, nor can it be done completely AFK. You can make it work manually, but you will have to be present to queue the group. You will need, of course, more than one Honorbuddy license.
1) Load WoW client A
2) Load Honorbuddy client A
3) Select custom class (if you have one other than singular) I recommend singular.
4) Click on class config
5) Set movement to "AUTO" and targeting to "NONE"
6) Save and Close
7) Select Dungeon Buddy
8) Click Bot Config
9) Select dungeons you intend on queuing for (aka Random Mists of Panderia Heroic)
10) Click Plugins
11) Enable refreshment detection, drink potions, and auto-equip
12) Select weapon style in auto-equip
13) Repeat steps 1-12 for second account
14) Invite your toon to group.
15) Queue for dungeon
16) Press start on both bots.
They will run the same dungeon together. When they finish, they will both leave the group. Just stop the bots. Re-queue. Then start them once more.
Caveats:
Make sure you select the right specs when you queue.
Dungeon buddy is not perfect, beware if you intend on AFKing.
FYI: I do this daily-even on LFR. It works.