This works for accounts on ibluetext.com and in our apps (iBlueText: Messaging CRM for iPhone and Android). You can also delete your account inside the app: More → Settings → Delete account.
We delete it within 7 days. We keep only what the law requires, such as payment and invoice records (kept by our payment processor, Stripe) and records of opt-outs, so that numbers that asked not to be texted stay protected. Questions: russ@ibluetext.com.