Many of the kits and tools described in the PHB (p. 154) state something like:
Proficiency with this kit lets you add your proficiency bonus to any ability check you make to create [visual disguise | physical forgery of a document | etc.]
Are there rules somewhere for what kind of ability check you would make to do those things?
It's not explicitly specified which ability you would use to employ these tools. Ultimately, it's up to your DM which ability is used for any ability check, and the default matching of skills to abilities is only a default. Both the Player's Basic Rules and the PHB include this section in Chapter 7:
Variant: Skills with Different Abilities
So it is up to your DM to decide which ability or skill applies to any ability check you make. With tool-based ability checks, this is even more the case, since they don't have the defaults that skills come with.
However, the 2 tool proficiencies in the question are both included in the list of examples of potential Intelligence checks.
Other Intelligence Checks.
The DM might call for an Intelligence check when you try to accomplish tasks like the following:
- Communicate with a creature without using words
- Estimate the value of a precious item
- Pull together a disguise to pass as a city guard
- Forge a document
- Recall lore about a craft or trade
- Win a game of skill
So the developers must have thought using these tools would generally be Intelligence checks.
As Miniman's answer suggests, both pulling together a disguise and forging a document are listed under the Other Intelligence Checks section of the Ability Checks guide in the PHB, so that would be the default.
This might, for example, be a History, Nature or just a generic Intelligence check (with a DM-supplied DC), representing the need for some kind of special knowledge (remembering exactly what a certain race is supposed to look like, or knowing all the right names to include in your document, or remembering what someone's handwriting looks like, etc.) to create the disguise or forgery effectively.
In some cases, I could see a DM requiring a Dexterity check (instead of or in addition to the Intelligence check) to see if you are physically capable of the fine control required to copy someone's handwriting convincingly, apply detailed makeup, etc.
Under the description of Deception checks, one of the examples is pass yourself off in disguise. Thus once you've created the disguise using the kit (and most likely an Intelligence check) you may still need a Deception check to pull it off.
5th Edition really encourages the role play aspect so it leaves the skills pretty much up to players and the DM to discuss. There's some interesting options here, but there's nothing really hard set in the rules as a guideline for anything. Basically, the best you'll find is the DC check table for actions:
Simple - 0 DC
Very Easy - 5 DC
Easy - 10 DC
Medium - 15 DC
Hard - 20 DC
Very Hard - 25 DC
Nearly Impossible - 30 DC
But again, it's a role play thing. So if you could logically do something with a disguise kit, then you run it by your DM to see if it makes sense. A Rogue who's proficient in disguise and forgery should be able to easily impersonate a town official for example. However impersonating the captain of the guard would be a lot harder due to the lack of muscular strength and body bulk.
