Is there any way to tell if a Pokemon is about to run away or is prone to running away?

Pokemon give no visual indication of being about to run away.

However, Pokemon such as Abra are (still) almost guaranteed to run following a failed capture attempt. The chance any given Pokemon will run away on the first throw (without any sort of modifier) is given in the BaseFleeRate variable from the decoded ProtoBuf file.

Additionally, Pokemon with orange or red rings have a higher initial chance of running away. All Pokemon will run after enough turns have progressed, as the chance of a run increases each unsuccessful turn.