Is 'a.k.a.' an acceptable abbreviation to use in academic writing?

If you're using it "literally" (i.e. - to specify an alternative name used naturally by [at least some] other people for the thing you're talking about) then it should be fine in most formal contexts. Except where the alternative designation itself is inherently informal (e.g. G W Bush aka "Dubya"), where it's a matter of whether mentioning the alternative name is appropriate, rather than aka.

What's not okay in academic contexts is the informal use of aka to introduce an ad-hoc alternative term purely to describe/characterise something - such as, for example, Houston's new Astrodome, aka. the Eighth Wonder of the World.

The above link includes a single period after aka, which I would say is never "correct". But although there are twice as many written instances of "[Alcatraz] Island, also known as The Rock", if you check the abbreviated usage it seems to me most writers don't include periods.

Wikipedia Manual of Style, for one:

a.k.a. AKA Should only be used in small spaces. Otherwise use the full phrase. … Never use aka.

http://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Abbreviations