。
The conversation keeps going further and further off the rails.
Literal
Derailment [subject-が] more-and-more escalate-[going-ていく].
脱線 'derailment' (literally coming off the tracks, from trains) is the standard metaphor for a conversation getting off-topic. どんどん is a mimetic for progressive, increasing action ('more and more, steadily'). エスカレートする is a loanword-plus-する verb. The auxiliary ~ていく signals a change projecting forward in time away from the present — paired with ~てくる, which points toward the speaker. Subject omitted in translation because 脱線 is itself the topic; English needs to supply 'the conversation' to fill in.