i don't know how Jaxx works but if you have access to your private keys and if you really had any bitcoin balance in those keys before the 1st of August then yes you are the owner of same amount in bitcoin cash.
spending those bitcoins *after* August 1 doesn't change anything about how much BCH you own. it has replay protection which means your BCH won't be lost if you spend bitcoin or vice versa.
Thanks for the explanation as I am currently having the same issues as to claiming my BCH. But based on this explanation, it then means that even if I transfer my coin to a say blockchain.info wallet in other to empty the previous wallet by following the procedures posted by Theymos, am I still good to go or is there a threat whatsoever due to that since I will be importing my keys into Electron cash in other to claim the BCH.
If you send your btc to different wallet, and import private key into Electron Cash you are good. There is nothing that can happen to your BTC, if your private key gets leaked or smth like that only thing someone can steal is your BCH