I've used a variety of python HTTP libs in the past, and I've settled on requests as my favourite. Existing libs had pretty useable interfaces, but code can end up being a few lines too long for simple operations. A basic PUT in requests looks like:

payload = {'username': 'bob', 'email': '[email protected]'}
>>> r = requests.put("http://somedomain.org/endpoint", data=payload)

You can then check the response status code with:

r.status_code

or the response with:

r.content

Requests has a lot synactic sugar and shortcuts that'll make your life easier.

Your data is already a JSON-formatted string. You can pass it directly to requests.put instead of converting it with json.dumps again.

Change:

response = requests.put(url, data=json.dumps(data), headers=headers)

to:

response = requests.put(url, data=data, headers=headers)

Alternatively, your data can store a data structure instead, so that json.dumps can convert it to JSON.

Change:

data = '[{"$key": 8},{"$key": 7}]'

to:

data = [{"$key": 8},{"$key": 7}]

Quoting from the docs

data – (optional) Dictionary or bytes to send in the body of the Request.

So this should work (not tested):

 filepath = 'yourfilename.txt'
 with open(filepath) as fh:
     mydata = fh.read()
     response = requests.put('https://api.elasticemail.com/attachments/upload',
                data=mydata,                         
                auth=('omer', 'b01ad0ce'),
                headers={'content-type':'text/plain'},
                params={'file': filepath}
                 )