Acts 11.4: 4 But Peter began speaking and proceeded to explain to them in orderly sequence [καθεξῆς], saying....
Peter's speech in Acts 11.5-17 proceeds in a naturally chronological order, with one remembered flashback in verse 16. If the analogy with Luke 1.3 holds, I suggest that καθεξῆς in the context of a narrative account, at least, can imply a chronological order.
ETA: That is, although terms like καθεξῆς are capable of implying a literary order other than strict chronology, they may still imply a chronological order as the most appropriate kind of literary order for narratives.