How can I ensure that the email is correct for each person on LinkedIn?

Nothing is guaranteed. If you can determine the naming convention for the organization the individual works for (such as firstname.lastname@orgname.com), you have a better chance of it being correct. RocketReach does refresh data pretty frequently as well.

RocketReach has standards of accuracy, but if you want to ensure the validity, utilize a program such as DeBounce or Zerobounce to run the list through.