Ok so i assumed this would be the place to ask if you guys need more detail let me know because I'm keeping it vague. First a background, My mom did a DNA test through Ancestry.com the results came up and found out she had an older sister she never knew about. Fast forward a few months, she is talking to her father and my grandfather about it and they thought they were talking about the same person but when my grandfather said he was their and the wrong date of the sister my mom had found through ancestry.com meant there was more than one. So where would I look for birth records in Kansas. I know the date, location of birth and the name of the birth mother that is it.
This is a question better suited for /r/genealogy. It is an active community and the people there should be able to better help you.
Otherwise, this explanation of Kansas birth records from the Kansas Historical Society gives a rundown on what records were kept in Kansas and where you can find them.
Also, be aware that the family trees that people post on Ancestry.com are very, very unreliable. A lot of the trees jump to huge conclusions that are wrong. You really need to do your own tree with an unbroken paper trail to be sure it is done correctly. Take anything written in those trees with a grain of salt until you've seen the evidence yourself. Even if there are a hundred trees saying the same thing, it's not very good proof of anything because most of the trees on Ancestry were just copy-and-pasted by one user to another without anything backing it up, further perpetuating the erroneous information.