The book Ann Dwyer's Easy Waters of California North, 2000. describes the 64 miles of Feather river from Oroville to Verona. This section of river is rated as class I-II whitewater. This should be suitable for sit-on-top kayaks paddled by people with some experience in river boating.

Additional rivers for kayaking are described in my Kayaking Guides for Whitewater Rivers in California.

If you are taking your sit-on-top kayak on the river for the first time you may want to get some training in a kayaking class and join a kayaking club. Even on a gentle section of river there may be some hazards that should be avoided. Training classes and river trips together with more experienced boaters are recommended for best safety.
How to get started in whitewater river kayaking - BRT Insights.