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 (http://www.google.com/products?q=old+work+box+ceiling&rls=com.microsoft:en-us&oe=UTF-8&startIndex=&startPage=1&rlz=1I7ADFA_en&um=1&ie=UTF-8&ei=bYajTL-dJIGBlAfg6cjKBA&sa=X&oi=product_result_group&ct=image&resnum=3&ved=0CC8QzAMwAg)

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.