Don't think so, at least not on the default chrome browser. You would have to install a different browser with extension support (Firefox definitely has it, and possibly others). Then you can install userscripts with Tampermonkey as usual.
I see, I might try Firefox then, and any way to make a backup of what was marked as read? I want to use it mostly for series that have too many doujin to keep track of, like Touhou, so it would be good to have a backup in case shit happens to my device.
Also, a userscript to open all pages at once like kissmanga is viable?
There is no need to backup, since the script just reads the lists stored on your Dynasty account. You can install it on your phone and it should auto sync when you first visit the website. If you meant that you want to backup lists in case Dynasty disappears forever from the internet (god forbid), that is also possible and I can provide instructions for that if you want.
However the script only checks for updates to lists on each device every 24 hours, so if you mark a chapter read on your phone it might not show up on your PC until the next day and vice versa. You can force a resync immediately by clearing browser cookies. Not the best multi device experience I know, I've been working on a way to sync more frequently without taxing the website too much for large lists.