It is the same as using a Repeater Region to heal with.

You need one of: Healbot, Vuhdo, or Grid + GridCustomLayouts.
This gets you a set of frames, with an alphabetical (fixed order) sort.
So the top frame is the same character on every screen.

Then set your interpretation addon (Grid needs Clique, while Healbot/Vuhdo do this themselves) to recognize a given click means cast this spell.

In IS Boxer, set a hotkey for the Character Set, to bring up the GUI in game.
In game, press the hotkey and go to the Repeater Region tab.
Choose a target, which will probably be either All Of (DK Team Name) or an Action Target Group (which you would define in advance, and drag your DK character names into the group).
The target is who will receive the click.
Create the region, drag it over the Vuhdo/Grid/Healbot frame; resize it so the shaded portion covers the entire frame (the border portion is not broadcast).
Click Sync, so the region is the same on all screens.
Save it as "Auto", which means it will be loaded on its own, whenever this character set is launched.

That gets you an auto loaded region of the screen (which overlaps your Grid/Vuhdo/Healbot), which when the mouse is in, sends the clicks (including modifiers) to the chosen recipients.
And your addon interprets say Alt + Left Click to be cast Death Coil at that target.

For a team like DK's, I'd probably use all of the team as the target.

But for a team like Shammies, an Action Target Group might be a better target, because you can use another mapped key to add or remove toons from an ATG.
So you could have a mapped key, which puts your shammy into their second talent spec (Resto) and removes the other Shammies from the ATG.
And on another press of the mapped key, puts your shammy into their first talent spec (Elemental) and adds all Shammies to the ATG.
So you can run with Tank + 3-4x Shammies, as Elemental with everyone healing or go with Tank + 1x Resto + 3x Elemental, and have only the Resto do the healing.