I haven't watched Samurai Flamenco's but apparently there is a character who claims to be in a long distance relationship with his girlfriend. It is only revealed in the final arc that his girlfriend has gone missing, and the text messages from the girlfriend is actually those he texts himself to keep his sanity.
To be honest, that's exactly my thought before I heard of Samurai Flamenco. The text messages that was supposed to come from Miyuki feels too formal and sketchy. We never see him texting back. Another suspicious detail is that none of Kindaichi's friends, from Kenmochi, Itsuki to Saki seem to have met Miyuki recently. They only hear about her from Kindaichi.