We moved in the August before he started school. Which in affect made it the furthest school.
Well, that's not the fault of the LEA and not grounds for appeal. You presumably then put in a late application for schools nearer the new address, but your son was placed in a school near your old address. Did you then get on waiting lists for nearer schools?
He would of got a place at this school as its 0.3 miles away from our house and he has a supplement form.
If he had been living at that address at the time of applications/place allocation, yes possibly, but he wasn't - again, not the LEAs issue nor grounds for appeal. What do you mean by a supplement form? That he was a sibling? This pushes him up the waiting list, but won't get him a place if there isn't one free.
The fact he would have got a place had you had the address at the right time is irrelevant. The appeal has to look at the decision that was made at the time it was made, with the information the LEA had at that time, and it doesn't appear from what you have said that they have made any sort of error.
The appeal also falls under the fair access protocol as he has no school.
That's not what makes it FAP. He had a school place and you withdrew him from it; at that point the LEA's responsibility to you ended, and it became your responsibility to find him a school.
If that school place was more than 2 miles/45 mins by transport away, then you have a stronger argument that they made an error in not finding something closer once you had moved, or considering him under FAP once you had made them officially aware of your new address if no nearer school had a place. Was the distance in excess of this? Were any other schools offered once you made the LEA aware of your move?
You also need to bear in mind that consideration under FAP doesn't necessarily mean a place at the school of your choice. The LEA will place a child under FAP at the school they consider best placed to take an extra, which won't necessarily be the one you want.