Conway, Jones and Tanghal bring Super-Team Family to an end with issue 15 (March/April 1978). They bring together the Flash and the New Gods in a mediocre story, which just leaves one wondering why Fastbak, the speedster of the New Gods, wasn't simply used instead.
After an opening in which we see the Flash with Metron, Lightray and Jezebel hovering around Orion, whose giant form is floating above the Earth, we get a flashback to how this all came about. The four New Gods were hanging out with Highfather in between adventures in their revival series when a "water-demon" (looks like one of the Deep Six to me) attacks Orion. They defeat the creature, but secretly he infected Orion with a growth virus, which has made him expand to the size of a moon.
Metron comes to Earth to recruit the Flash, figuring he will be fast enough to enter the Source and find a cure for Orion. The only possible reason that they get the Flash to do this, instead of Fastbak, is that Metron must not really think it will work, and doesn't want to kill off Fastbak.
Darkseid is the one behind this all, which is hardly a surprise. When he learns that Metron has recruited the Flash to help them he sends out one of his warriors to try to stop the hero.
The New Gods take the Flash out to the area of the Promethian Giants, those who tried to enter the Source but became giant sized as a result, now forming a sort of wall as a barrier.
The Flash defeats the Apokoliptian warrior, and although there is some cool art I am not exactly sure what wound up happening to the guy.
The Flash entering the Source is about as un-thrilling visually as it could be. He comes back with a machine that cures Orion, but remembers nothing of his time in the Source.
Darkseid is pissed that his plan failed, Iris is pissed that the Flash is late for dinner, and Metron is pissed that the machine crumbles to dust right after being used. So it's sort of an unhappy ending for most of the characters, and a poor note for the book to go out on.
There was one additional issue set to go, a team up of Supergirl and the Doom Patrol. Since the series got cancelled at this point that story was serialized in Supergirl's series in Superman Family.