how do I add my Chromebook to my Apple icloud account so I can increase the storage on my chromebook?

Not sure that you could, nor would really want or need to add the Chromebook.

However I doubt a non-Apple product may be added to your Apple ID + iCloud.

You may consider increasing storage by looking into additional storage capacity

on another online service, such as google offers online. Figure in the bandwidth

costs & transaction speeds to accomplish accessing stored items of size online.

A Chromebook revelation by a Mac user | Macworld

A Chromebook revelation by a Mac user ... I can use iCloud for documents and

have no qualms about recommending a Chromebook instead an Apple laptop.

macworld.com/article/3101401/hardware/a-chromebook

An example, for image storage you could get & use google Photo app, among

other things offered by that brand. Additional storage capacities will cost you

no matter which device you may use online. + That may be akin to vaporware.

At any rate...

Good luck & happy computing! 🙂