How do I file a civil union divorce for gay couple who are living in different states?

Use of a lawyer is recommended.

Florida does not recognize gay marriage, and therefore will not grant a divorce to a couple lawfully married in a state that does recognize gay marriage. If the state in which you presently does not recognize gay marriage, and therefore offer gay divorce, your options are limited. If the state in which your former partner resides does recognize it, you may be able to work out an agreement and then invoke the jurisdiction of the court in his state based upon their residency there (if they meet the residency requirements). If neither of you reside in a state that recognizes gay marriage and therefore gay divorce, it is more complicated. You should consult with an attorney.

This is a very complicated area of the law and is ever changing. The place to file, if possible, would most likely be where they last resided together. What you need to do is actually go see an attorney, face to face.

Your question indicates that you are in Texas. I'm not sure where your estranged partner is, but Texas does not recognize a legal marriage between individuals of the same sex. If you two own property together or have children together, you will probably need to seek remedies to address those issues in court. However, you may need to get formally divorced in whatever state you were originally married in because there technically is no divorce option available for gays and lesbians in Texas. Speak to a local attorney about the particular circumstances surrounding your marriage to determine what the best course of action is for you to take.