Style guides differ on how to render film titles. The Chicago Manual of Style, for example, recommends using italics, whereas the AP Stylebook recommends using quotation marks. However, I can't think of any style guide that recommends using either italics or quotation marks on first mention but neither on subsequent mentions.
I have seen books that use boldface or (more often) boldface italics for the first mention and simple italics thereafter, but in that case the boldface is being used to signify "first mention" and italics to signify "film title."
With regard to your comment that "over-use of italics would spoil the flow of the text," my view is somewhat different from yours. Once an author has established the practice of using italics to identify film titles, I find it distracting to encounter the title in plain roman type later on; to me, switching from italics for film titles on first occurrence to no special treatment for them on subsequent occurrences amounts to underusing italics, just as including quotation marks on first occurrence but then dropping them on subsequent occurrences would amount to underusing quotation marks.
Once you've trained your readers to recognize that you are using italics or quotation marks indicate a film title, I don't think that you need to worry that applying the convention consistently will be distracting to readers or in any way harmful to the flow of the text.
Best Answer
Aka doesn't need italicising. It can be written and will be understood both with and without periods, although I see it usually written without.
Style guides will differ on the periods. As a counter-example to the somewhat heavyweight CMOS, the Guardian recommend to use aka without periods. Unusually, the guide also shows it in capitals, but a quick look in the paper shows nine lowercase aka without periods and one uppercase AKA without periods. (Edit: I asked the style guide editors and they recommend AKA because it's pronounced as individual letters.)
So: italics are not needed, and follow your own style guide (if you have one), or pick a style and apply it consistently.