I am using 2 similar ES methods to load and delete documents:

result = es.search(index='users_favourite_documents',doc_type='favourite_document',body={"query": {"match": {'user': user}}})

And:

result = es.delete_by_query(index='users_favourite_documents',doc_type='favourite_document',body={"query": {"match": {'user': user}}})

First one works ok and returns expected records.
Second one throws Exception:

"TransportError(404,'{
\"found\":false,
\"_index\":\"users_favourite_documents\",
\"_type\":\"favourite_document\",
\"_id\":\"_query\",\"_version\":1,
\"_shards\":{\"total\":2,\"successful\":2,\"failed\":0}}')"

What am I doing wrong?

I'v used version 6.2.0 of the Elastic Stack and the use of the API works for deleting like this:

es.delete_by_query(index="index_name", doc_type='doc_type', body={"query":{"match": {"message": "message_value"}}})

if your value is INT remove the "" in message_value.