My parents want to add me as a owner of their banks, and they still have income going into those bank accounts this year, I wanna know the tax implications on my returns.

If there is more than one owner on the account you would have to ask the bank whose name and social security number will be used to send IRS documents like interest payments which would be taxed. 

I cannot give you legal advice  however adding a child's name to any property or bank account  is usually not a good idea ... if the child has an auto accident and gets sued they can attach any asset the child is listed on ... instead setting up a trust with the child as a trustee may be a better idea or just being put on the account as an authorized signer and not an owner of the account.   I highly recommend you seek a local attorney and see what you can do legally in your state.