Firstly, you need to (via console only currently) in "Binary Support" add "multipart/form-data".
This is the Content-Type used by POSTs that include files.
Next, in your code you need to parse the request body itself. Python provides a simple function for this : cgi.parse_multipart
from cgi import parse_header, parse_multipart
from io import BytesIO
def post_file(event, context):
c_type, c_data = parse_header(event['headers']['Content-Type'])
assert c_type == 'multipart/form-data'
form_data = parse_multipart(BytesIO(event['body'].decode('base64')), c_data)
However, it loses the filename along the way.
It's theoretically possible, in theory, to also use the cgi.FieldStorage, but I haven't tried yet.