Import a mkv file to premiere or after effects isn’t possible. But it’s not needed to convert the mkv to other format. It’s enough to extract the video and audio files from the mkv file. That’s because ‘mkv’ is only a container, not a real video format.
I use mkvtoolinx and imkvextract to extract those files. You need to install mkvtoolinx, which brings a command-line software called mkvextract that allows to extract the files from the mkv. If you want you can install and use imkvextract (a fronted of mkvextract for mac) is pretty easy, and in a few seconds you’ll get large video files from the original mkv.