I have a checkbox question where a user can select up to three checkboxes. Based on their answer(s) I have to create a follow up question for each checkbox they selected. (So there may be up to three follow up questions).

Is there any way to do this using Limesurvey Logic?

You will have to create as many additional questions as there are checkboxes in the first place. Then you need to use conditions or the expression manager to hide/show these questions depending on the respective responses.