First of all, to any sarcastic viewers: this phobia is very real and very horrifying to have. Trying to make light of it or just saying "Well they're not real" is of no help and in fact can just make things worse. I beg the internet for empathy and understanding on this.
Now. How to get better, according to my personal experience.
If you want to cure your phobia without medication, take it in small steps. First learn calming techniques and practice them often in every day life. Breathing techniques were most effective in my case. Once you have mastered this, create a list of steps to achieve for yourself. Mine went as follows:
1) be able to hear or read something about these undead.
2) Accomplish saying "Zombie" every now and again while remaining calm.
3) Have someone find not very graphic pictures to view on occasion and slowly move on to the scarier stuff.
4) maintain a conversation involving something Zombie related.
You can accomplish each of these goals with continued use of calming exercise.
Eventually build you way up to perhaps seeing a movie or something of the like. And remember, having someone who takes this phobia seriously that you can talk to is an immense help. Be sure to let them know if they just need to listen, or if you are actually seeking feedback for specific questions. It's important to be clear and concise as to what you require to overcome how this phobia effects you personally.
Breathing I found was the best way to fight off the fear, strangely enough. When you start to panic, your breath becomes shallow and your heart rate picks up. However if in that instant you actually force deep breaths into your lungs it slightly calms your heart beat while making your brain realize that you still have some control. Once you've established this control over one of your body's basic functions, you can slowly take control of your fear.
Hang in there fellow Kinemortophobians or ambulothanatophobians, ect as you prefer. And remember, the definition of a phobia is "irrational fear". It isn't supposed to make sense, but you can still beat it.