Bash script which downloads the latest linux stable kernel
Good stuff:


Yay for putting your code on github.  I see a lot of folks afraid to wait until everything is perfect to do that.  But having the backup and history of git is too handy to wait like that.  So I love seeing somebody doing that from day 1 of a project.
Yay for use the double square bracket form of if and checking for common mistakes.
Yay for using env.  As you can see from my github I'm not so great at this one, but it is a good idea.


Suggestions:


Move common code into a library.  Your EUID check is the most obvious culprit.  To create a shell library you should create a file of functions and then source it into each of your commands.  So to translate your check into a function is easy:

function validate_root {
    if [[ $EUID &gt; 0 ]] ; then
            echo "You need root privileges for this script."
            exit
    fi
}


Then use the library later like so:

source lib.sh

validate_root # be root or exit

Move common data into the library.  The most common item is /etc/latest-kernel... what if you want to move it somewhere else?  If it is in a variable in one place it will be a lot easier to do.  There's no reason not to throw those into the common shell library file too.
It looks like you made a cut and paste error on purgelatestkernel but since I can check out the github version I can see what you meant there.  Generally you're not supposed to edit code during code review put I think you'd be ok to fix that part up since you're not altering the code you meant to review.
Avoid duplicate code by looping in the install:

for file in lk create_etc_lk purgelatestkernel
do
        echo copying $file to /usr/bin
        cp $file /usr/bin
done


This also makes it easy to add other things like a validation of permissions or check for return values without insane amounts of error-prone cut and paste.
Instead of having the option for a prompt be something that requires a source code alteration why not make it conditional based on a variable that possibly could be altered with a command line option?