Why didn’t Shaquille O’Neal win any championships in Kobe Bryant’s prime Lakers teams if he is so dominant as some claim him to be?

He did win during Kobe’s prime. If Kobe’s prime is defined to be 2001–2013 (which is where he had his best statistical output), then Shaq won 2 rings when Kobe was in his prime.

Just look at Kobe’s 2001 season. He averaged 28 PPG in the regular season and 29 PPG in the playoffs. That’s as good or better than any of his later years. He was already in his prime by 2001.

Now if you’re saying why didn’t Shaq win any championships when Kobe wasn’t in his prime? Well first recognize that 2000 Kobe was maybe not his full prime form yet but definitely on the way there. And Shaq completely dominated the league and playoffs that year.

Ok, so what about 1997–1999? Well, two reasons here.. their team wasn’t mature enough yet, and Del Harris wasn’t a great coach.
They fell to the Jazz in both 1997 and 1998. Karl Malone matched Shaq evenly during both series. The difference was Nick Van Exel and Eddie Jones / Glen Rice and Kobe coming off the bench got outplayed by the Jazz trio of Byron Russell, Jeff Hornacek and John Stockton and Jerry Sloan outcoached Del Harris.
In 1999, the Spurs swept the Lakers. Tim Duncan outplayed Shaq during this series big time. People really need to put more respect on Duncan’s name. People always think of Shaq as the better scorer than Duncan right? Well in 1999, Duncan put up 29/11/3 against Shaq who put up 24/13/1 and swept Shaq’s team. Duncan was dominant if his team needed him to be. I mean David Robinson only averaged 13 PPG that series! It was mainly Duncan that gave it to the entire Lakers team. Oh, and also Pop >>>> Del Harris. That much should be obvious as well.

In 2000, Phil Jackson joined the team and transformed the team, got Shaq to actually try on defense and improve his footwork, Kobe evolved another gear, and the rest is history. People also need to respect Phil Jackson more. Without Phil, Jordan’s limit was the ECF (with a solid coach in Doug Collins), Without Phil, Kobe’s limit was the 2nd round (with Mike Brown). With Phil he reached a combined 13 Finals and won 11 of them. That shows you Phil Jackson’s impact.