I've managed to so by using:
timeSlider.watch("timeExtent", (evt) => {})
In the event I've found the current time of the the timeline, using that and featureLayer definition Expression property I was able to make use of the timeSlider with client side featureLayer.
Timeline widget allows you to view temporal data from web maps, feature layers, and map service layers to see how data changes over time.
For connecting client Side feature layer requires either a geocode service or a hosted feature layer. So to my knowledge that is not possible out of the box
I've managed to so by using:
timeSlider.watch("timeExtent", (evt) => {})
In the event I've found the current time of the the timeline, using that and featureLayer definition Expression property I was able to make use of the timeSlider with client side featureLayer.