Loki was just too young (probably around 20 years old, about 7 years old in giant's years) and Xebec probably had a policy against infants joining his crew. Kaido was already a teenager (15 years old) who looked like a young adult IMO. And even after +/- 10 years of war experience, Kaido was still only an apprentice under Rocks.
About Linlin being scouted by the WG at 6 years old and Loki being ignored as a 20 (7) years old, they were in two different positions. Loki was Elbaf's royalty, while Linlin was an "orphan" (actually a foundling) directly under the (probably) most relevant child trafficker of the world. It's the same as why they didn't scout Roger, Whitebeard, Oden or even the admirals (they just joined the marines in adulthood, most of them by their own free will) as children, the WG was either unaware of them or they weren't "available" for the taking.