The product you are describing is the 4th Edition Dungeon Master's Kit
This was released midway through 4th edition's release and included a book as well as some maps and tokens. Unfortunately it is out of physical print. You can buy the book only as a digital PDF here.
There is no "Dungeon Master's Kit" for 5e that has been released or is scheduled to be released before Christmas 2014.
Keyword is "kit" which generally means a book, some dice, and some tokens/figures to aid in the visual representation of play.
The 5th Edition Dungeon Master's Guide will release shortly
The DMG will be out December 9th. It is simply a book, a big one, covering lots of rules and providing a ton of setting and optional rules for 5th edition.
4th edition and 5th edition are similar but different
Both tell stories about heroic adventurers but the framework they use to tell these stories and engage the players is different. There is a tonal shift in focus for the rules between editions. The 5e DMG is not compatible with the 4e books.
Buying all 3 books will ensure your son and his friends will be able to play the new edition.
If you do pick up the 5e Player's Handbook, Monster Manual, and Dungeon Master's Guide they will have everything they need to play 5th edition.
There are a few official miniatures out for 5th edition currently but they are not available online.
Wizkids partnered with WOTC to make plastic miniatures for 5e, but they seem to be only available in game shops. You may want to check out a local game/hobby shop as they have these or other fantasy miniatures that he could use.
However any miniatures your son already has are perfectly usable with 5th edition.
Proceed with Caution, you are entering dangerous territory.
Expanding inspiration in this manner will make it more powerful (by definition). Adding dramatically more options to any ability will do this.
There are also some soft differences between granting success versus granting failure. All party members succeeding once will have a very different feel than a monster who fails four to six consecutive checks.
But these aren't the biggest threat you're going to face. That one belongs to the pure casters...
Save or Suck
While an attack roll on a spell versus a saving throw for its target often seems like an arbitrary distinction, they aren't always. There is a category of spells often referred to as "Save or Suck," which almost universally favor saving throws instead of attack rolls. Spells like Hold Person, Banishment, Feeblemind, Entangle, and Polymorph all inflict near-catastrophic effects on a failed saving throw.
Under your proposed house rule, an optimal tactic would be for players to transfer their inspiration to the full casters in the group (Wizard, Cleric, Druid, Sorcerer), who then uses it to cast repeated save or suck spells on any monster who stands above the crowd.
This has two very negative consequences:
Players are now under social pressure to transfer their inspiration elsewhere, rather than using it to help their own characters shine.
"Boss" fights become incredibly difficult to stage, as any boss has to deal with multiple saves against incapacitating effects with disadvantage applied.
This is not a fatal flaw...
This is not a fatal flaw to the house rule. Monsters written to be boss monsters typically have auto-save abilities, because even without disadvantage save or suck spells are pretty devastating.
In addition, exploiting it requires players to play at a somewhat optimized level. I would not be surprised for an individual group to either not see this tactic, or to be chivalrous about not exploiting it.
But be careful. Make sure that everyone involved is aware that you may back this change out early if it causes problems.
Best Answer
To players, mechanically, Inspiration is a token you spend to gain advantage on a roll, and that’s all it is. You can only ever have one of these tokens in your possession, which is incentive to use Inspiration up quick and not hoard it. You can also pass that token to others, so you might do that if you’re about to get a second one.
The true reason Inspiration exists, though, is this: it's a mechanical reward for playing the way the Dungeon Master appreciates. The guidance is thin, and that’s what it comes down to, though the guidance doesn't say it in such explicit terms. To support saying that, I’ll quote in full everything (everything) from the Basic Rules about how you acquire Inspiration, barring the example, found on pages 35-36:
That’s all the guidance there is in the Basic Rules. The guidance suggests to use Inspiration for roleplaying consistent with one’s character sheet, but then gives the DM the freedom to choose to award it however they want:
So given that, and the fact the DM is the only one who can create new Inspiration, the entire mechanic comes down to being a device to encourage the players to play the way the DM wants.
That can be used to constructive or destructive ends. People are going to have Opinions about how Inspiration should be used, and what ways are good or bad, but the Basic Rules guidance begins and ends at the above. That guidance certainly seems to fit in with D&D’s established notion that the DM has precedence over the players, and enhances that idea.
Inspiration could be used like Fate points, and awarded as compensation and reward for a player making a mechanically suboptimal choice. (Apparently, the Starter Set suggests as much!) However, D&D 5e presently lacks pretty much all of the mechanical support and a large amount of play guidance that drives Fate points working the way they do. Note the conspicuous absence of “the players can suggest they should probably get it” in the guidance, for instance. Choosing to use Inspiration this way is entirely a choice of the group. The management of Inspiration can also be made by group cooperation, but again, that’s a choice of the group.
It seems the authors could have included Inspiration to be a solution to all those complaints of “my player isn’t roleplaying consistent with their character’s alignment and story!” - since then the DM just penalises that player with no Inspiration whilst they’re doing that. I have Opinions on whether this is healthy for the game, and so will others.
At the end of the day: consider whether there’s behaviour you want to encourage in your game, and if it’s healthy to provide mechanical incentive for players to behave that way. If so, use Inspiration for that.