In order to get this to be seamless, I would guess that this only works when you are sending from one yahoo account to another one correct? Unless they have found a clever way to share the public keys.
Today our extension works as a developer only demo, and no Yahoo keyserver service is online yet. If our toy keyserver code didn't make it into this release, you will see it very soon and will be able to experiment.
We released the source so we can solicit security feedback early, and can keep all security and privacy critical parts of this product in the open. No "just trust us" now or in the future.
Along those lines, we will work with industry peers to build public key registry software that interoperates with other federated providers, is open source, and is transparent in the cryptographic sense. I.e. Yahoo and Google users should be able to send encrypted email to one another with ease, and if either company was forced to lie about the public keys of our respective users we would be caught because math.
There's a lot more in the works, and we have many challenges to overcome to make this generally usable. In addition to the key server, there's not unnecessarily breaking existing mail features, multi-device issues, search over encrypted content w/o providers being able to read it, and mobile support to start.
If you know anyone with the skills and motivation to make strong, usable encryption available at internet scale we'd love to listen, collaborate, or hire. :)
I do know a team whom you should work with: keybase.io
Keybase.io have an early-level product which would help with your keyserver issue. It has a CORS-enabled API, a commandline tool, an online interface for encrypting, signing, verifying, etc. and a "ring of trust" tool that follows the modern social network model (where, you can "track" somebody and it auto-signs their keys each time they upgrade.
There is already published docs that show Yahoo is/was part of Prism since 2008: http://www.wired.com/2014/09/feds-yahoo-fine-prism/
Your actual worries at this point are the key exchange (impersonation) and extension distribution.
The first is very hard to get right without alienating a large number of potential users, the second seems perfectly possible to have verified but seems like it's going to require some kind of changes in the Chrome extension system.
It'd be great to come up with some kind of way to also tell the client what resources are expected, and if a new one is loaded (e.g. <iframe src="http://dangerous.malware.com"></iframe>) the client would not even connect to it.