Take a look at short artilce Knee Pain: Treatment Based on Individual Evidence.  It discusses thought process on selecting particular treatment intervention i.e. tape.

Damien Howell PT, DPT, OCS - www.damienhowellpt.com

I assume by "kinesiology tape" you are referring to "Kinesio Tape,"  which is a product originally developed by Japanese chiropractor Kenzo  Kase nearly 30 years ago. It is different from traditional athletic tape  in that it is intentionally elastic, and very different from "ace"  bandages in that it is backed by adhesive and designed to support and  mobilize the skin while the wearer is moving, especially during athletic  activity.

Kinesio tape was designed to help prevent  and assist recovery from injuries that benefit from increased lymphatic  flow around the injury site. The lymphatic system is an important  conduit of immune system activity, which can be critical to the  maintenance and repair of damaged tissue. Since most of the lymphatic  system is right underneath the skin, the simple application of this kind  of tape helps to circulate lymph by resisting or enhancing the movement  of the outer layer of skin over the underlying tissues.

The  following link is courtesy of Kinesio competitor "KT Tape," and details  the application of this type of tape by a physical therapist on an  athlete/model to address hypothetical medial knee pain...

I've  had this kind of tape (Kinesio brand) applied to my own injury before,  and can vouch for its effectiveness. You can find it at sports or  medical supply outlets, or online. The video uses probably far less than  a dollar's worth, and each application can last a few days through  showers, since the tape is waterproof. Pre-cut lengths of tape cost more per foot than cutting your own from a roll.