Probably. 7-Zip won't work, but I'm sure that there are other file unzipping tools for chrome OS. I'm not familiar with chrome OS, so I don't know the file system works on it. But as long as you can download the correct version of flashpoint and make another file folder to extract the files to, you should be good. Make sure to follow all the instructions on the Old Island Directory and hopefully it'll work. That's about the best advice I can give you.
I'd recommend using an ad blocker (I use Fair Adblocker https://www.standsapp.org/?utm_source=AppWindow because you can use it to only limit not outright block and white list sites) and before you use a link first open the current poptropica and log in then while thats still open click the link to launch the old poptropica
There’s an app for both poptropica and poptropica worlds, but the poptropica one doesn’t have all the islands. It still has most of them though. I know you said links don’t work but try this one https://play.google.com/store/apps/details?id=air.com.pearsoned.poptropica&hl=en_AU