I've been told that in the next update to ArcGIS Online, the map viewer will support a configurable refresh interval. You might look for that capability and use AGOL to view a web map rather than relying on a Flex-based map viewer. If you can live with a user needing to pan or zoom to force a display refresh, I suppose that's another option, but I don't have any good high-level suggestions for avoiding the display flicker/flash when you need to frequently and programmatically refresh feature layers to update a map display.
I know that the Operations Dashboard was developed using the Windows WPF SDK for ArcGIS Runtime. That choice of development platform may be what's providing the ability to smoothly update features on the display, but I really don't know. That development is handled by another team; if you're interested I can probably find someone who can discuss the technical implementation. Every other client application map viewer I've seen tends to flicker or flash when the feature layers are updated.
There are techniques a developer can use to "blit" graphics from a secondary buffer into a primary graphics buffer. Basically you're building an image from the feature data and then copying a prerendered image to the graphics buffer being used by the viewer. That's really low-level graphics manipulation though, not something that you'd be able to do using one of the Web APIs, Flex in your case, to build a simple map viewer.