None is returned because the get_linked_docs method needs different parameters than what you are passing it.
params = {doctype, docname, linkinfo, for_doctype}
Doctype and docname you can easily get. Linkinfo can be fetched from get_linked_doctypes method of linked_with.py module.
from frappe.desk.form.linked_with import get_linked_docs, get_linked_doctypes
linkinfo = get_linked_doctypes(doctype)
docs = get_linked_docs(doctype, docname, linkinfo)
print(docs)