So, I think this is the relevant section from the overall Yahoo! APIs Terms of Service:
Data Collection, Storage, and Use.
You may not retain or use, and must immediately remove from any Application and any data repository in your possession or under your control any Yahoo! user data obtained through the Yahoo! APIs not explicitly identified as being storable indefinitely in the API Documents within 24 hours after the time at which you obtained the data, or such other time as Yahoo! may specify to you from time to time, including pursuant to notification received from application uninstall event handlers.
You may not share GUIDs (Global Unique Identifiers) with any third party.
We're a bit picky about any user data, but there actually is very little user-private data in the Fantasy Sports APIs. So I'd say the most important thing is not to share GUIDs, and I'd be hesitant to suggest that there's any reason for you to be storing user-generated information like league names, league passwords, team names, message board posts, or anything else that the user would have submitted to our site. If you do end up storing that data, it feels like something where you should be periodically purging it if you detect that the user has revoked your permission to use their data (ie, if you can no longer renew their access token).
We also have restrictions about player statistical data, where you really shouldn't be storing that for any reason that we can imagine. I'm not sure that would stop you guys, as that is fairly useful information, but we'd tend to say that you shouldn't hold onto that stuff and you shouldn't, like, build your own stats repository site on top of it or anything.
If you're a bit more detailed about what you're thinking about holding onto and why, I can probably give more specific advice.