Both basement laundry tubs are filled with water. After bailing water and getting tubs dry,I discovered that water from the kitchen sink (directly above tubs)is flowing into them. What should I do?

Well it doesn't actually flow into those tubs but they share a common, backed up, drain line. You need to rod out the line after the tub trap enters the next main pipe. There will likely be standing water in these pipes for a while.

Since your laundry sink and kitchen sink share the same common drain, you could snake the line from the kitchen sink vent on the roof. Put in at least enough snake to reach the bottom floor plus 20 feet, or more depending on where the next nearest main fixture drain ties in. If Snaking from the roof is not plausible , then snake from downstream of the laundry sink trap as ball suggested. Just make sure the snake goes down, not up the vertical drain pipe.