Each month I pay my parents $300 so they can support themselves. My father still works and so is my mother. They filed a joint return themselves. They DO NOT live with me.
Can I get any tax benefits for my monthly payments to my parents?
The only way that I know that you could get a tax benefit for yourself is if you could claim them as dependents. That would let you get an exemption for them, which isn't a lot anyway.
The fact that they don't live with you does not matter since they are your parents and there's an explicit rule allowing for that. (https://www.irs.gov/publications/p17/ch03.html#en_US_2015_publink1000170951) You would still need to show that you provide more than 1/2 their support, that their gross income is less than $4000/yr, and they would have to file separately unless they met the exception on that one. (https://www.irs.gov/publications/p17/ch03.html#en_US_2015_publink1000170857) Sounds like none of those apply in your case.