Manually - I.E either mount system r/w with something like Remount from GP, then install the apk, or drop the apk in system/app & set permissions (either in shell or with Root Explorer/similar) to 644 (rw-r-r) ?
Might not work/have problems with recent versions of Flash though, not supported officially on Android anymore & on a 3 yr old device you're not guaranteed to get it working.
Edit - If you use terminal to do it, don't forget to switch to root first.