How to give Airplay traffic priority on network? I noticed that when I download a large file over Wi-Fi my Airplay stream stutters and then dies out.
I am just streaming audio from MacBook Pro 5,3 (e.g. Spotify) to my Airport Express.
At the same time a Xiaomi Redmi 2 and a Huawei P9 are often connected to the Airport Express. No heavy traffic is going to them (only some WhatsApp and browsing) 

During the download, data is coming in at around 6 MB/s, and I see that 200 KB/s is going up.

When I check my Wi-Fi statistics I see I have a transmission rate of 145 (Mb/s I assume), which converts to 18 MB/s so I should have plenty of headroom.

How can I give Airplay priority on my network, such that there's always plenty of bandwidth available to stream?
I don't know how to fix your issue but i can help you to go around it.
So if you have the wifi 5GHz (dual mode) you can put your playing device on that network and the downloading device on the 2.4GHz network. This somehow helped me to fix the dropouts while watching videos online.

my config is: iPad playing music via airplay audio, macbook Pro downloading a video. airport express with dual wifi.

It is not the final solution neither the solution you are looking for but it helps in some cases.