Flying Blue allows new members to claim miles for flights up to 3 months previously:
1.3.4 Qualifying Flights taken or used no more than 3 months prior to the signing date of the application form qualify for earning Level and/or Award Miles and should be claimed retroactively as per the retroclaim rules defined in 1.4.6.
However, you would need to check the earning rates for the
booking class of your AR flights, and for the
booking class(es) you expect to use on China Eastern, as cheaper fares may earn fewer (or no) miles.
I don't know the details of other ST FFPs, and hence I can't advise whether other programmes might be better suited for you.