I've never heard of LoA before actually, but from reading the posts that have already been made, it doesn't seem to have much merit to it. If I'm reading correctly, then it's...positive thinking, you could even say that it's similar to prayer. I was particularly interested by Poptart's comment, "You attribute the things that DO come true to the Law of Attraction, and dismiss the ones that didn't," Definitely sounds like prayer to me. And in my opinion; no matter how positive your thoughts are, you can't change reality, to a degree. A person with diabetes, being very positive while shoving cake in their face is likely going to go into a diabetic shock and possibly die, but perhaps that's a bad example, you can judge that for yourself.
Either way, I'll never look at my transition this way, because gender isn't JUST how you think about yourself. Sure, you can think, "I'm a man," all you want, but if you still look like a woman on the outside, you're going to be called a woman when you're in public, and there's nothing that you can do about it.
Also, no matter how much time I spend thinking, "I wish I had a dick," It's never going to magically sprout from between my legs without the help of testosterone and possible surgery. As far as transition goes, what good is positive thinking if you can't change your body? Sure, it can help get you out of depression; but so can watching a good movie, a stupid joke from a friend, or a bar of chocolate.
I don't know much at all about this LoA, but it sounds ridiculous to me, why give it such a mystic name if it's nothing but, "Keep thinking positively!"