Looks simple enough. First, get a strobe light. It should be bright enough to really make a good effect.
Placement of the light is also very important. I would be sure that it is placed both well above head level and behind the people as the approach the prop. You never want people to actually see the strobe light itself.
I'm not sure what triggers the prop, but there is something, either a motion sensor, or breaking a beam or stepping on a mat. (Do you have a link to the actual prop from where you ordered it from?
Find whatever it is that turns on the prop. use that same trigger to turn on the strobe light. Without knowing anything about the prop, it's hard for me to give you specifics. If the prop itself runs on 120VAC then it probably plugs into a box that acts as the trigger which turns on the prop when someone comes near. Just add the plug for the strobe light (probably an extension cord that goes to the strobe light) to the same output that feeds the prop and they will both switch on and off at the same time.
If the prop runs on DC, then you need to figure out what voltage it runs at, then get a relay that has a coil which works with that voltage, and turn on and off the strobe light by having the relay switch it on.
I know these instructions are all very vague, but I am happy to give you VERY detailed instructions as soon as I can learn more about the actual prop. Please post a link to it and I'll try to get some info on how the prop turns on and off and what kind of power it runs on. Once I know that, I can come back here and give you detailed instructions and a parts list if you like.