So, if you take 40 years to forge 10 kingdom claims, then you're running a lot of risk as to whether you'll be able to successfully use them all before your time runs out.

Your forged kingdom claims will not be inheritable. What this mainly comes down to is gambling on your character's life expectancy. You can repeat this potentially many times! Repeat the process of claiming a duchy, forging another kingdom claim, seceding again, etc. instead of warring for the kingdom you just claimed, instead offer fealty to another kingdom you'd like to pick up. Once you have the claim, declare a war of independence on your liege and win to secede. Now you can fabricate a claim on the kingdom. Switch your primary title to the duchy which is a de jure vassal of your liege. This might require some preparation from earlier to do quickly. Now that you're inside the kingdom, take whatever territory you need to form or usurp a duchy that is a de jure vassal of your liege. If they have high enough crown authority to prevent internal wars, that will block you, so either pick a different kingdom or be prepared to first defeat your liege in a war to lower authority. Offer fealty to the king of whichever kingdom you want to start with. Wait until you inherit as a very young ruler. Optionally, start preparing for your later wars by inviting some claimants. Grab as much land as you can everywhere, such that you outmatch actual kingdoms, but stay as a duke. Get yourself set up as a very powerful duke. This can lead to a rather complicated but potentially very effective strategy for world conquest: If you are a powerful duke with your primary ducal title being a de jure vassal of the primary kingdom title of your liege, then you can plot to fabricate a claim on the kingdom.

Ck2 how to get claims on kingdoms