Dogs like to chew on almost anything: bones, balls, remote controls, their own tails—you name it. But back when A Dog's Purpose is set, PetSmart hadn't been founded yet. If a dog wanted a fancy chew toy, he needed his owner to make one.
Ethan, going for his Dog Toy Crafting merit badge, makes a toy for Bailey that is "like a cross between a boomerang, a Frisbee, and a baseball" (10.18). We're not sure what's wrong with any of those toys individually, but hey, whatever works. The Frankentoy isn't much of a hit with dogs or people; according to Grandpa it's "Not aerodynamic […] Too much resistance" (10.27). Whenever Ethan pulls it out, Bailey "glance[s] away in dread" (13.8).
Even though it's a bigger disaster than Nintendo's Virtual Boy, the toy means a lot to Ethan. He's playing with it when he first meets Hannah, he uses it to break a window to save himself from a fire, and he saves it all the way up until his death. When Ethan looks at it, he doesn't even seem to be thinking of playing with Bailey. Instead, "he'd hold it up and look it over, feeling its heft, and then put it away with a sigh" (13.8).
It seems like Ethan is thinking about his own life—and about his own failures—when he looks at the toy. Like his life, the flip is heavy, it didn't quite work out as he planned, and Ethan isn't sure what to do with it.
One of Ethan's last actions is to toss the flip to Buddy, the reincarnation of his dog Bailey. Dying of a brain aneurysm, Ethan heaves open the window and throws the flip outside. Buddy gets it, but in Ethan's dying brain, he imagines he's playing with his dog Bailey one last time. He's reliving the happiest moment of his childhood, and in his final minutes, he gets to relive it without the weight of his adult life suffocating it. Can you get that from a dog toy shaped like a hippo? No, that's the magic of homemade memories.