Blaine is Red and Leaf’s grandfather, you’re right! He has one child, a daughter named Scarlett, who left her home on Cinnabar Island to go on her pokémon journey to challenge the Kanto Gyms in the year 3584. During her journey she runs into Professor Samuel Oak’s son, Charlie, and his best friend, Aiden, who are travelling together. While Charlie was undertaking a junior research program during his journey, Aiden was a competitive trainer like Scarlett, so the two naturally became rivals. Aiden and Scarlett both had ambitions to become the Champion one day and while they competed, they also end up becoming friends, especially after Aiden unexpectedly helps save Scarlett’s life (which is also when her crush on him fully blooms – though it takes a while for Aiden to notice both that and his own feelings for her.)
The two end up dating and later get married. Scarlett moves to Pallet to be with her husband and the two have two children together – Red and Leaf. While both still had aspirations to become Champion, they both found that that goal was harder then they had thought when they were young. Scarlett ends up with health problems following Red’s difficult birth, which result in her needing to stay closer to home. She gets a job as a teacher for aspiring trainers at the local school. Aiden, meanwhile, gets a job as a trainer at the Viridian Gym, however when Red is 8 and Leaf is 6, he goes missing following his discovery of Team Rocket activity there. During these struggles, Blaine does his best to support his daughter and her family, though he can’t often leave Cinnabar due to his job as Gym Leader. He also, of course, ends up facing his grandchildren years later when they both go on their own journeys and is very proud of what strong trainers they’ve become. While Blaine was somewhat distant for them growing up, he is able to establish a better relationship with his grandchildren once they’re teens.