I think from the Law of Attraction's point of view, we should not try and overcome these emotional responses as this is our inner being's (infinite intelligence) way of telling us that we are on the wrong track.

Instead, we should utilise these emotional responses to guide us to the right track. Let's say that you are scared of swimming and when you have tried to give swimming a go before, you went completely numb and couldn't do it out of fear. I would interprete this as your inner being telling you that you should not attempt swimming yet. In other words, the fact that you are feeling fear implies that the outcome is not going to be a good one if you do try and swim. When the right time comes, you will feel an urge to do it and that is when you should do it.

Actually, the fight or flight response is more commonly associated with the hypothalamus, although the amygdala apparently plays a role. The amygdala is primarily responsible for moderating the laying-down of long-term memory patterns in the brain.

Minor anxiety can be controlled with relaxation exercises such as meditation. Exercise works well too, as does eating well.

If anxiety is severe enough to negatively impact your life (i.e. panic attacks), there are medications that can relieve the symptoms.

Beyond that, check your attitude, examine your beliefs, and see if some of them are not serving you well. Look here for more about this.

"The most important question you'll ever ask is whether the Universe is a friendly place."

-- Albert Einstein