Why doesn't Kana's boss know about the Day of Flight?
In episode 7, Reki states that she was despondent after Kuramori's disappearance. Nemu tried to cheer her up by doing research at the library to find an explanation for the disappearance. This explanation ends up being the "legend" about the Day of Flight at the library. Thus, information about the day of flight must be openly accessible.

In the same episode, Rakka tells the cafe owner that "Kuu has left us." In response, the cafe owner asks if Kuu has disappeared. After that is confirmed, he says, "But that's how you Haibane are, right?" Thus, Kana's employer is not an anomaly if he knows about the Day of Flight and other details about Haibane life. With the rest of the content in the exchange with Rakka then, it looks like Torisuda's suggestion (that the employer is aware of the Day of Flight on some level and simply didn't want to explain in detail) is relevant here. (After all, the details in his exchange seem too accurate for mere speculation.) It's still possible that he doesn't actually know, but what I'm trying to assert is that the scenario where he does isn't improbable at all.

However, it's worth noting that not all of the townspeople are familiar with Haibane life. In ep. 5, Sumika tells the presumably teenaged Rakka that she does not look like a newborn, despite being good friends with Nemu. Similarly, in ep. 8, a woman in the thrift store treats Rakka in a somewhat objectifying way, which might be grounds for assuming a lack of familiarity with the Haibane.

Thus, it must be then that the Haibane are "separate" enough that a number of people get by without ever having any meaningful interactions with them, while a small number do (and thus might be more familiar with Haibane life).