Can staph infections be transmitted by kissing?

Unlikely. Whereas staph aureus infection can be transmitted by skin to skin contact, the higher concentrations of staph are in areas such as inside the nose, moist areas of the skin where two skin surfaces meet such as underarms or groin. In addition the protective benefit of saliva also decreases the possibility of lips as a source.
Could be. If you had an infection around the lips, it would be possible. However, staph is a ubiquitous organism, that is, just about everyone has it on their skin. It is a very common cause of skin infections.