KIT

KIT is a quick way to ask others to "keep in touch." For example, a friend, family member, or colleague might use this acronym near the end of a chat, email, or DM conversation to ask you to continue writing to (or otherwise contacting) them.

Typically, people who use KIT to mean keep in touch are people you do not (or soon will not) see often. That's why these people are asking you to continue writing and/or calling them, as it's the only way they get to talk to you. Of course, most people are quite bad at keeping in touch with anyone except their family and BFFs - so the person who sent you KIT probably won't take it personally when you inevitably fail to do so.