Either could be correct.
Which verb form to use is primarily just a stylistic choice - but regardless of whether the context is formal or informal, Past Perfect might be preferred to enhance the "narrative" aspect of the speaker's utterances (is it part of a longer description of some extended event, as opposed to simply reporting that single action?). Interestingly, in your specific context, the Simple Past version has in fact become by far the most common in recent decades - so if anything, that's the "better" choice.
You might say that the perfect is redundant because the anterior (past) meaning is conveyed by "after". Yet they both sound acceptable. I've been trying to think of how there might be a difference in meaning. For some reason, the past perfect seems to convey a slightly greater sense of "completion" of the first item. The effect is very subtle.
There is a potential subtle distinction, as alluded to in my previous comment. Basically, it's that using Past Perfect here establishes (or "reminds" us) that there's a "narrative reference time" in the past (when we were flying the kites) which the speaker is primarily interested in talking about (where the eating of lunch came before that reference time). The subtle effect is to draw the audience into casting themselves back into the time of kite-flying, which in principle might make for a better "story / narration". But it's only a "potential" distinction.