There appears to be no junction box in this old 1950s home. Can this be right? To install a new flush mount fixture will I first need to install a junction box? If I cut through the plaster and slats (current hole in plaster is small and close-fitting around socket) how will I be able to secure the junction box?

Try this:
old work box ceiling - Google Product Search

What Strat provided is great, but keep in mind the box he provided is only for a light fixture.

If, by chance, you are installing a ceiling fan, the box needs to be rated for a ceiling fan.