Pipe strain may be absorbed by a flexible pipe coupling. However the flexible pipe coupling must be properly installed. Installing a flexible pipe coupling in the line without any support will not achieve anything.
The most effective use of a flexible pipe coupling is to anchor the end of the coupling closest to the item you want to protect.
If you want to protect the pump from movement of the piping, then anchor the end of the flexible coupling that is closest to the pump. This will allow the piping strain to be absorbed by the pipe coupling, but the flange on the pump side of that coupling is anchored, therefore no strain is being passed to the pump.
Should you desire to protect the piping from movement of the pump, the you must anchor the end of the flexible coupling closest to the piping. This will allow expansion of the pump flange to be absorbed by the pipe coupling, but the flange on the piping side of the coupling is anchored so that the strain is not passed to the piping.
Flexible couplings are not a cure for a poorly designed and installed pump system. A properly designed and installed pump system will not make a pump move wether there are flexible couplings installed or not.
Refer to the attached installation instructions.