To get the Magic Boomerang, you must fuse Kinstones with the four Tingle Brothers (although one of them is David Jr., who isn't actually related to the other Tingle Brothers, even though he bears an uncanny resemblance to them).
Part 1: Fuse Kinstones with Tingle
To start off the quest, you must fuse Kinstones with Tingle, and then talk to Tingle again to find out about his brothers. Tingle hangs around South Hyrule Field (near Smith's house), and you can only reach him after you have obtained the Cane of Pacci from the Cave of Flames. BE SURE to talk to Tingle again after this first Kinstone Fusion, because otherwise his brothers won't appear in their respective places around Hyrule.
Part 2: Fuse Kinstones with Ankle
Ankle is sitting on a ledge in the Lon Lon Ranch area. You have to get the Lon Lon Ranch key to get access to the pasture, and from the pasture you will need to go into a cave and push some blocks around after splitting in two (so you need to have two elements powering up your sword). Remember, if Ankle isn't there, you should go talk to Tingle in South Hyrule Field. Once you fuse Kinstones with Ankle, a tree will open in North Hyrule Field that has a switch inside. More on that later.
Part 3: Fuse Kinstones with David Jr.
After getting access to the Lon Lon Ranch pasture, you can access Lake Hylia to the east. Find Stockwell's house here (there's a dog inside) and David Jr. is nearby, sort of southeast from Stockwell's house. Fuse kinstones with him.
Part 4: Fuse Kinstones with Knuckle
Once you have the Mole Mitts, you can dig into the cave in Trilby Highlands. There's a ladder in that cave that leads up to where Knuckle is sitting.
Part 5: Go to North Hyrule Field and Flip the Switches
Now that you've fused Kinstones with all four of the Tingle Brothers, you can go into the trees that opened up in North Hyrule Field and flip the switches in the cave in each one. After doing so, a ladder will appear in that cave. Go to the center of North Hyrule Field and climb down the ladder, and you will find a chest containing the Magic Boomerang!