Disc brake rotor compatibility and recommendation I have Ultegra BR-RS805 flat mount hydraulic brakes on my gravel bike, and Shimano RT86 6-bolt Ice Tech 160mm rotors.

There's a shim between the brakes and the frame to fit the 160mm rotors. When the guy at my LBS looked at my bike, he held the brakes and rocked it back and forth and said there was a lot of movement on the back wheel due to the shim and recommended that I use a 140mm rotor instead so I could remove the shim. As I have another set of wheels I'm building out for the bike, I thought it made sense to get a pair of 140mm rotors and then use those on the two rear wheels, with the 160mm rotors on the front.

As the RT86 rotor does not come in a 140mm size, would a 6-bolt 140mm SRAM Centerline rotor be compatible and a good option?
This doesn't answer your question, but your problem before the question. 

If your brake body is moving about, the problem isn't the existence of the shim (which is used by all brakes when they upsize) but either:


the bolts holding the shim/adapter to the bicycle or the brake to the adapter were not properly torqued and loctited. 
the bolts holding either the shim or the brakes are too long and are bottoming out so they can't lock down properly 
the shim was poorly made and has a defect that is causing it to move
your bike store is either incompetent or trying to upsell you something


Note that brakes are supposed to move when the bolts are slightly loose so that you can properly center the pads against the rotors. Then you clamp them down to the proper torque tolerances. 

Since most people want to go up in rotor size to have more effective braking, you'd be bucking the trend in going down. Are you 100% confident in the mechanical skills of your LBS?