Yes, blockchain is a thing, but it's 2018's buzzword du jour. It's what the "i" prefix was a few years back, when it was used on every goddamn device you could fit in your pocket. Legal Fling is using the word in its promotion entirely in the hopes of appealing to the tech bro lizard part of your brain that maybe doesn't know how to use a copy machine, but still has a smart thermostat at home and is just waiting for its chance to become a Bitcoin gazillionaire.
Blockchain is essentially the public ledger through which all cryptocurrency transactions take place. It's a massive permanent digital record that cannot be altered without many different people seeing you do it. Legal Fling wants to use this, piggybacking on all those cryptocurrency transactions, to toss in a digital code that relates to you getting your hump on. You and your would-be paramour use the app and consent to sexual relations. That consent gets encoded in the blockchain forever and always, a memorial to your decision to engage in coitus or other sticky activities. Romance isn't dead!
If you don't see the problem, please consider how clumsily it bungles the very idea of consent as it works in the real world. You don't just contractually agree to a menu of sexual escapades in advance. What if you change your mind? What if things get weird right in the middle of it? Legal Fling lets you opt out later, but your initial consent is now permanent, assuming it was legitimately you who consented and not, say, a predator who took your phone. And are you supposed to ask someone who has transitioned from potential sex partner to maybe a rapist to hold up a sec while you update your consent contract?
Luckily, legal experts have already questioned how well any of this would hold up in court. I don't have a law degree, but I believe the American Bar Association would refer to it as "a goddamned trash fire."