ELS just means you weren't able to meet military standards, or adjust, or something similar. It's like being let go in the probationary period. Unless you were kicked out for criminal activity, with a court martial conviction along with it, there will be no affect on getting your EMT certification or license.
I have an ESL and I have been in ems for over 20 years. Yes, I have not been able to apply for a few jobs mostly a couple fire departments that say "must have an honorable discharge" but other than that it has not been an issue. Good luck