Is that a project you saw? Need to go back there to ask question. If not, I don't think that would work or look good.
Why do you want to put vinyl on baseboards?
What is your goal? My best guess is to clean with alcohol and then slowly apply. Press carefully. It will be a pain if the baseboard is not smooth.
Are the baseboards in bad shape that you want to cover? Are you just trying to change the look? Vinyl would be a painstaking task to put on a baseboard. Why not paint them or use strips of pre-pasted wallpaper to change the look. Wallpaper is so much easier to work with than vinyl. You can cut a long strip, soak and place in no time if that is what you are aiming for.