Darren Gold had a stomach virus the first time he used an app called Heal to summon a doctor to his Beverly Hills home. He liked the Stanford-trained doctor who showed up so much that he called Heal again when his 2-year-old son had a fever, and again when the whole family had colds.

The charges—$99 each for the first two visits; $200 for the family—weren’t covered by insurance, but Mr. Gold, who owns a corrugated-box company, says that was still a bargain compared with taking time off work to go to the doctor. “Now, whenever...