How do I get access to my keychain when I don’t have access to my iPhone?

Did you sync your Keychains with iCloud? If so, they would be available with any of your other Apple devices that you log in with the same Apple ID.

Ref: How to find saved passwords on your Mac – Apple Support (AU)

laquetta86 wrote:

My iPhone is currently sitting in rice after some time in the pool.

Placing a potentially liquid-damaged phone into rice or any other type of desiccant will not work and only make things worse by adding additional debris into the phone.

Despite that it is supposed to be water proof

No iPhone is waterproof. Only water resistant. Sorry, but that's not the same thing, and its resistance rating was determined in controlled laboratory conditions. Apple does not recommend using their iPhones in water (or any liquid).

I’m using my wife’s tablet and need to access some of my accounts on her iPad. I went to the iCloud website but no keychain.

Do you both share the same Apple ID? If previously enabled, the keychain associated with your device & Apple ID would be stored in iCloud.

Ref:

• Set up iCloud Keychain – Apple Support (AU)
• Everything you need to know about iCloud Keychain - iMore