If he has ever had a jab past the point of the ones he recieved as an infant this defence will not work. The magistrates have seen it all, he would need a sustained history of refusing treatment due to his phobia for a defense like this to be successful.
This would not be simply saying no, this would be a phobic response to the GP even suggesting bloods being taken. A phobia is not a simple fear, it is a full panic/vomiting/fainting situation. If there is no evidence of this on your brothers record this defense will not wash. As other users have pointed out, if he has a tattoo or piercing this defense is dead in the water. Not to be blunt, but this defense is already dead in the water. It's a tale as old as the hip flask defense and it does not work. Do not listen to drink drive specialist solicitors, there is no such thing as specialising in the petty session. They are vampires for lack of a better word, they prey on hopes and always deliver nothing. Regardless of their 100% success claims, as pointed out they don't count the cases where they tell the defendant at the last minute to plead guilty. As many users of this forum have paid upwards on 10k to find out.