As of February 1, 2019 LinkedIn's zip file export is not working correctly for many users. The downloaded zip has only 3 or 4 .csv files that only have the basic profile & recommendations information in them. It doesn't have any important information like positions, education, skills, projects, certifications, honors etc.
The correct zip file has typically many .csv files in it based on the number of sections you've in your LinkedIn profile. Please check your downloaded zip file and in case it only has up to 4 .csv files, then you'll get only limited information imported to your Resumonk resume.
Please tweet to @LinkedInHelp or contact their customer service and request them to fix this issue urgently.
We've also raised it with them but if more users complain about it, hopefully LinkedIn will fix it sooner.