Airlines allocate only a small number of seats for air mile tickets on each flight so it helps to be flexible with your travel dates. However, you will still be liable for the airport taxes which usually comprise a large proportion of the overall ticket price, so even with air miles your ticket will not be completely free.
We recommend that you book the best possible fare available to suit your holiday itinerary and then redeem your miles on other merchandise available to you - car rental, accommodation and so on. You will need to arrange your own flight arrangements with the Frequent Flyer programme concerned.