All provider levels at and above EMT-Basic have intramuscular medication administration as a required skill. EMRs are below that level of training, so it’s not required training for them, but they can get it as an optional training.
DHS has a webpage discussing the utilization of EMS personnel in Public Health Immunization Clinics: https://www.dhs.wisconsin.gov/ems/h1n1.htm
The advice there is for the Service Director or Medical Director to reach out to the local public health office to partner on immunization projects. The easiest method is for EMS personnel to become (temporary) paid contract employees or volunteers of the PH Department. Or the PH Department can assist the EMS agency with getting registered with DHS as a vaccination entity.
DHS also has a "COVID-19: Program Information for Vaccinators" webpage with an FAQ, links, and other resources for potential and current vaccinators. They host a "weekly office hours" every Tuesday morning, and there's a link on the page. The url is https://www.dhs.wisconsin.gov/covid-19/vaccine-program.htm .
EMS agencies would, like other vaccinators, bill either the private insurance of the patient for the administration fee, or bill Medicaid/ BadgerCare. Almost all EMS agencies are set up for medical billing for the services they provide.