Measure the width of the horizontal ledger board sitting at the top of the wood fence. Make sure that the rail planter -- a planter that straddles the width of a board -- will sit snugly over the horizontal board. A planter filled with soil and plants will be heavy. Don't position the planter right in the middle of a panel of fencing as it might cause the ledger board to sag in the middle.
Check to make sure that the fence posts are strong with no leaning or wobbling to them. Check that the rails of the fence that the pickets are nailed to are firmly nailed to the fence posts. Check for any softness in the rails or rotted wood. Setting a planter on a flower box holder that hangs off the fence rails will place a lot of added weight on the fence. The fence post and rails must be strong enough to handle it. Even more weight is added to the planter when it rains or the planter is watered by hand.
Go to a greenhouse and look at the flowers that will go into the planter. Measure the height of the various plants, then choose a planter that fits in with the height of the fence plus the height of the flowers at full bloom. Consider whether they will block out the various views to the rest of the yard.