Is it possible to fry breaded or flour covered chicken with only butter?
Yep, you can fry anything in just butter. You only need to know that whole butter has a lower smoke-point (~350F,177C) than a lot of other oils, so it needs to be done a bit slowly.

See this Smoke Point Chart: (the last column involves fatty acids, not relevant here)

Higher smoke points of course mean the oil can get hotter without burning. For what it is worth, slow frying in butter is often an awesome way to cook anything. It tastes great.

Clarifying butter brings the smoke point up to over 400F (205C), but you sacrifice some flavor that way. Exactly how hot you can get clarified butter (or unclarified butter, for that matter) depends upon several factors, including how it is manufactured and/or clarified.

If you're looking for breaded, bone-in fried chicken ala KFC, don't try to use butter, it would be problematic to keep the breading adhered at such a low temperature. It would have to fry for a very long time. I suspect the breading would get greasy and fall off. Plus, that much butter would be really expensive for cooking oil that can't handle multiple uses.

If you are looking to deep fry whole (bone in) breaded chicken thighs, for instance, it's pretty much unheard of (but not impossible) to do it it butter. However, butter can be great for breaded, boneless chicken breasts.