I preface this with saying that I am not an attorney but have researched this for my own oldest child when we were considering having my husband adopt him. With the birth father not being on the birth certificate, there are no rights to terminate. If he wasn't listed on the birth certificate, and he hasn't been adjudicated paternity in court (meaning you never went to court where a judge entered in a judgement that is the father), there is no legal father.
To do a step-parent adoption you will have to prove to the court that the person you believe to be the father has been notified of your intent to have your child adopted. If you know his address, that will be accomplished by having him served with court papers. If you have him properly served and have proof of service and he doesn't respond to those papers in the time that they say, that will probably be the end of it and you will be cleared to move ahead with the rest of the adoption. If you don't know where he lives, you can publish a legal notice in the paper of where you last knew him to live instead of having him served.
There will probably be other steps involved (in my state, step-parent adoption includes a home visit by CPS) but given that it seems that he actually has no rights, all you need to do is prove that he's been notified and give him the opportunity to respond, which it sounds like he won't do anyway.
I'm 99% sure you would actually file this in Texas as Kansas has no jurisdiction given that neither you nor the child lives there. Go to your local courthouse's clerk's office and ask. Those folks can't give you legal advice but they can be enormously helpful in letting you know what needs to be filled out by whom and in what order. Step-parent adoption can be a long and complex process so it's probably best to have an attorney help you with this.