You need a webcam. It can be separate from the computer though. LSAC has a pretty extensive list of what's allowed and not allowed in. the FAQs https://www.lsac.org/update-coronavirus-and-lsat/lsat-flex.
While studying at home I have my laptop propped up onto a laptop stand (pretty typical, ordered off amazon so I don't strain my neck) as well as a bluetooth mouse. Does anyone know if these items are allowed during the flex?