See http://kontena.io/docs/using-kontena/logs.html for documentation how logs are handled.
Usually it's a bad idea to start to couple log management things in the apps themselves, as you said also.
The logs are stored on Kontena masters DB, in a capped collection (kinda ring buffer).
Kontena 1.2.0 came with the option of forwarding the logs with
statsd protocol along with storing them on masters DB. I do not know Papertrail myself if it can take in
statsddirectly. If not there could be some intermediary (logstash, fluentd, ...) that "translates" to some other protocol which Papertrail accepts.
One other option is to configure each service so that Docker sends the logs directly to Papertrail with some supported protocol. There's three caveats here:
1) Kontenas own logs are not forwarded unless you make the
log-driver configuration on Docker level
2) As Docker will stream the logs directly, they are not stored on master at all. I.e. you cannot do
kontena service logs xyz
docker log xyz will be blank also as the logs are not stored locally on the node.
Yet another option is to stream the logs out of Kontena masters DB. For an example, see: https://github.com/kontena/kontena-log-archiver