ONYX General Purpose Boating Life Jacket Child, Red 30-50 lb $23.00 View on Amazon
Kids
Kids paddle boards and kayaks by age
Quick answerSize from the child's weight and height, not age: kids boards run 7'6" to 9'6", youth kayaks about 6 feet, and life jackets follow USCG weight classes.
Paddle board by age
Kayak by age
Kids boards, kayaks and life jackets
ONYX General Purpose Boating Life Jacket Child, Red 30-50 lb 
Airhead Youth Trend Life Jacket, Coast Guard Approved, Blue/Green USCG approved $35.99 View on Amazon
Owntop Swim Jacket Youth 50-90 lbs, Neoprene Swim Vest Kids, Lightweight, Quick-Dry, Buckles Zipper, Kayak, Swimming Training, Boating, Watersports (Fuchsia, M) 50-90 lb $43.46 View on Amazon
Stohlquist Child Life Jacket. US Coast Guard Approved Type II Infant PFD (20, 30 lbs) with Support Collar & Grab Handle. Adjustable Life Vest for Kids, Toddlers & Infants for Water & Boating Safety USCG approved $69.99 View on Amazon
Lifetime Shark Youth Kayak with Paddle, 6 Ft, Blue 6' / 130 lb max $129.04 View on Amazon
Sizing specs: Lifetime Shark Youth Kayak with Paddle 
Pelican Solo EVO DLX - Kids Sit on top Kayak with Paddle and Decals - Mango - Twin Tunnel Hull with Swim up Deck - Lighweight & Durable - 6 ft 6' $250.59 View on Amazon
Sizing specs: Pelican Solo EVO DLX On the water: Wear a properly fitted, USCG-approved life jacket every time, dress for the water temperature rather than the air, and check your state and local paddling regulations before you launch.
This is researched general information, not professional advice. Sizing figures are starting points: confirm against the maker's own sizing chart and the capacity printed on the boat or board.