When you complete the single-player Story mode you will then be able to scan the following Amiibo's to get the corresponding bonuses.
Callie
Perks
Faster Swimming
Faster Running
Faster Super Jump
Gear Unlock: Hero Replica Armour
Headgear
Clothing
Shoes
Inkling Boy (Blue)
Perks
Special Charge Up
Special Power Increase
Quick Super Jump
Gear Unlock: Samurai Amour
Headgear
Clothing
Shoes
Inkling Boy (Green)
Perks
Special Saver
Swimming Speed Boost
Faster Respawn
Gear Unlock: Squinja Armour
Headgear
Clothing
Shoes
Inkling Girl (Orange)
Perks
Ink Saver
High Recovery Speed
Faster Swimming
Gear Unlock: School Outfit Armour
Headgear
Clothing
Shoes
Inkling Girl (Red)
Perks
Enhanced resistance to ink and bombs
Gear Unlock: Power Armour MK1
Headgear
Clothing
Shoes
Inkling Squid (Green)
Perks
Faster Respawn
Higher Defense Against Bombs
Ink Saver
Gear Unlock: Power Armour
Headgear
Clothing
Shoes
Marie
Perks
Tenacity
Ink Saver
Special Charge Up
Gear Unlock: Armor Replica Outfit
Headgear
Clothing
Shoes