Turn your recliner over so you can easily access the parts underneath. Swing the reclining portion of the chair completely out.
Spray some lubricant on the offending metal parts and springs that affect the rocking or deployment of the footrest. This will grease any parts that rub together to create a noise.
Flip the chair back over and gently sit down, making sure your body is evenly filling up the chair so one side isn't weighed down more than the other side.
Swing the footrest out slowly to eliminate any further noise.