The official word on this question from the Developer of the Flexispy Software is as follows: ( taken from the flexispy.com website )

How can I tell if FlexiSPY is on my phone?

Solution FlexiSPY is not a virus and must be deliberately installed with a unique set of steps and configurations. It will not perform any functions that were not configured by human intervention. However, it does not install any visible program menus, folders or icons. Once installed, it may only be accessed or uninstalled by equally deliberate human intervention.

You should not let anyone that you do not trust access your device. However, there is no way to detect FlexiSPY once installed.

In practice we recommend that you consider the following:

Software programs such as Flexispy have remote monitoring and Flexispy cannot stop the phone from lighting up or flashing when phone monitoring is activated.

The GPRS and/or the internet connection icon activates for no reason.

There is an unusual increase in GPRS activity.

Software programs like Flexispy use GPRS to transfer the data logs

Some competitive solutions that use SMS fowarding  Your SMS bill has recently increased and you dont remember sending so many messages.

The final statement from Flexispy that “You should not let anyone that you do not trust access your device” is very practical advice raise a red flag if your partner asks for unusual access to you phone.  The Flexispy software cannot be remotely installed.