The most important thing when using the KeyChain is to not use kSecAttrAccessibleAlways
or kSecAttrAccessibleAlwaysThisDeviceOnly
because then data is not encrypted securely (see Apple's documentation). Not using these adds a layer of security to KeyChain data, but still, a strong passcode would be required by the user to protect his data. If the user has no passcode on the device, the data is unprotected. If the user has a 4-digit passcode (the standard), the data is protected very weakly and can be brute forced in minutes.
If you require protection from jailbreak (and other attacks), your best option is to not use the KeyChain, but create an encrypted sensitive data store of your own and require the user to have a secure passcode. Store the data encrypted using a key generated from that passcode.
This could inconvenience your users, so if you wish to provide a grace period between requiring passcode, think of a way to provide a session cookie to the app which is invalidated after a set period of time.