Using multipart/form-data with Power Query. This assumes that any files being uploaded are textual; changing this to support arbitrary binary data is possible, but wasn't interesting to me.

multipart.m

let
    Web.MultiPartPost = (url as text, parts as record) as binary =>
        let
            unique = Text.NewGuid(),
            boundary = "--" & unique,
            crlf = "#(cr)#(lf)",
            item = (name, value) =>
                let
                    filename = Value.Metadata(value)[name]?,
                    contentType = Value.Metadata(value)[type]?,
                    line1 = "Content-Disposition: form-data; name=""" & name & """" &
                        (if filename = null then "" else "; filename=""" & filename & """"),
                    line2 = if contentType = null then {} else { "Content-Type: " & contentType },
                    lines = { boundary, line1 } & line2 & { "", value }
                in
                    Text.Combine(lines, crlf) & crlf,
            body = Text.Combine(List.Transform(Record.FieldNames(parts), each item(_, Record.Field(parts, _)))) & boundary & "--" & crlf
        in
            Web.Contents(url, [
                Headers=[#"Content-Type"="multipart/form-data; boundary=" & unique],
                Content=Text.ToBinary(body)
            ]),
    fileContents =
"{""code"": ""15315""}
{""code"": ""526133""}
{""code"": ""43011""}
{""code"": ""83988""}
{""code"": ""182347""}",
    parts = [
        id = "c9c43e63-9372-441c-9ab7-c5e66d7da371",
        file = fileContents meta [name="upload.txt", type="text/plain"],
        locale = "en-US"
    ],
    Result = Web.MultiPartPost("http://foo.com/bar/baz", parts)
in
    Result

What is the purpose of creating filecontents when we are passing the file? should it not pick data from the file?

What is the purpose of creating filecontents when we are passing the file? should it not pick data from the file?

You could get the contents any way you wanted -- File.Contents, AzureStorage.BlobContents, etc.