MasterGwydion
Emperor Mongoose
Probably not. 1) the pursuing ships can't always just tell the Starport authorities what to do - unless they can. Most PCs can't, most of the time, but even governments will have jurisdiction issues. 2) the Starport may not have detected their jump Detection is rarely automatic, and it does not tell you anything about the ship. In a busy port you will get 100s of hits, so useless. You can check the transponder signals, of course, but if you are doing that, you don't need the jump flash. 3) By the time you get to check out any jump location, the ship is long gone. 4) the starport needs to have the equipment for this, which poorly resource facilities will not have. It doesn't really seem like something even a well resourced starport is likely to have. Local system defense or IN or Scouts will have this when the tech is available because clusters of ships jumping in during wartime likely signals an attack, but unless you are part of their organization, they're not going to share. 5) if the ship is evading the PCs or if it just need to go somewhere far out in the Oort Cloud, the signal might take days to reach the starport, so it will be a long time before you even get started on the search.
1) Have you never played a scout or an agent of the Imperium?
2) There are more starports controlled by the Starport Authority than there are capital ships in the IN. Are you trying to tell Me that a multi-million-ton starport doesn't have a gravity sensor? Automatic detection range on those is 1 parsec. Notice that it says "automatic detection range".
3) You are assuming that the ship left for another destination, which is by no means a guaranteed. Also, even if it did, if you can contact the Starport as in #1, they just ask where the ship went.
4) A GAS is the single most powerful tool for gathering information available to the Third Imperium. It allows them to track every ship in Imperial Space that doesn't have Stealth Jump.
5) Yes, that is possible, but all it does is delay the pursuit.
Okay, so you have come up with a bunch of edge cases where none of this would work, but in 90% of cases it will work for those operating the ships and starports or their agents, like the IN, IMoJ, the IISS, the SPA, megacorps and regional corps, etc. Hell, even the TAS can probably do it.
Your problem is that you are only taking the microview, the player-scale view. I am looking at the marcoview, how all of these different technologies can affect the setting as a whole, not for just player characters and individual ships. I mean, seriously, it is like you are suggesting that because you can't get access to flight tracking data from the airport, that airports shouldn't have that technology or that it shouldn't matter because even agents of the government shouldn't have access to it, because you can't?