Do I qualify for 240 hr visa transit?

Unfortunately, your itinerary is not eligible. The main section of 240 hour visa free transit scheme clearly requires that the immediate points before and after your mainland Chinese visit have to be in two different countries or eligible territories. Eligible territories are Hong Kong, Taiwan and Macau. As you can see, your both immediate points are located in one country - South Korea.

If you can, it would be useful to alter your itinerary to become eligible. For example, you could maybe think about introducing some other country or territory, for example Hong Kong. Like this your itinerary could look like:

South Korea - Kunming - Hong Kong - South Korea

An itinerary of the above type would be eligible for 240 hour visa free transit without any doubt. Now, it will be up to you to decide what will you do. Just to know, if you retain the original itinerary you would have to obtain a Chinese visa in advance. In the end, I encourage you to use correct terminology because this is not 240 hour transit visa, but 240 hour visa free transit, so there is no visa of any kind. Have a nice journey.