I don't entirely agree with GiddyPickle. The LA will have used special software known as a GIS to measure the distance. Unless you have several thousand pounds to spare you will not be able to use the same method yourself to check it. Any alternative method you use for measuring the distance will be less accurate.
You certainly need to know whether they have used straight line, shortest walking route or whatever. If they have used the straight line distance your only chance of disputing it is if you can show they have measured from or to the wrong point.
If they have used shortest walking route or similar you should ask the LA to confirm the route used and see if it actually is the shortest route. However, you need to check carefully what the admission criteria say about the route used. They may, for example, require that there is lighting along the entire route, in which case you can't suggest an alternative route using an unlit footpath.
As you are currently fourth on the waiting list you have a good chance of getting in that way. However, looking at your appeal:
How many classes do they have in Reception, Y1 and Y2? If they have 5 classes in total your appeal will be infant class size which means you need to show that a mistake has been made. However, if they have 6 it will not be infant class size and you will have a better chance of winning your appeal.
Do you have any reason to believe they have got the distance from your home to your school wrong?
Have you checked that your daughter was placed in the correct admission category?