High school student getting chemical engineering work experience?

In my view you need to get whatever job you can where there are chemical engineers or related disciplines ( eg industrial chemists or mechanical engineers). As long as you get the occasional opportunity to talk to them or try to work out what they are doing (won't be easy) or in other ways and get a feel for the environment in which they work. Doesn't matter if you are sorting drawings or providing refreshments for meetings, your good 'Sherlock Holmes' nose will fill in some pieces of a jigsaw puzzle. You may of course strike it lucky and get a firm willing to provide the appropriate information for someone considering a career in their company. Be brave though if what you find is not for you.