What is the best 'appliance' or tool to use to floss with a retaining wire in place? (permanent wire behind teeth after the removal of braces)

Threader. The floss threader is the best. I recommend the one by butler. It is a loop with a straight piece sticking out. Looks like fishing line. You put the floss through the loop and thread the straight end of the threader under the teeth and wire and pull it through with the floss. Another good technique is the "soft piks" or "go betweens "(small). Water pic is very helpful. Also, ultrafloss is good.
2 "bests" A floss threader (looks like one of those little wire needle threaders), may help thread floss between lower front teeth. Because the roots of the lower incisors are so close to each other, however, a floss threader may not fit. Try a water pik daily, never set higher than about medium. Excellent results reported in the literature, and in the hands of my patients.
Several options. There are many different aids to getting floss through in between your teeth at the local pharmacy or supermarket. Honestly the one that gets you to routinely use it without getting frustrated and therefore forgoing its use is the "best" one to use. Floss threaders that enable you to use regular floss are probably the most effective. "superfloss" by oral b is a great second one.
Also Try Platypus. I agree with dr thaler. There is also a floss pick called platypus that is designed to get around ortho wires that have worked well for many of my patients.
Floss threader. I recommend using a fine floss threader. Butler gum co. Makes a really nice one that is the thickness of fishing line. If you can't get floss through with a threader you can try a product from the same company that i believe are called floss picks or soft picks. They are small plastic picks with a green rubbery and textured material on their ends. You can also try interdental cleaning brushes.