A. I've done talking ― let's get started.
B. It's time we got started on the washing up.
In A, whether ‘started’ is transitive or not is dependent on further context.
In B, ‘started’ is intransitive.
Am I right in assuming as above?
Thanks in advance
In both cases, it's intransitive. The phrase can be transitive, as in, "here, let me get you started" or "let's get this party started!"
Also, it should be, "I've finished talking" or "I'm done talking."