Dockerfile and entrypoint which will automatically flush dnsmasq when host files in the /data directory changed

docker-entrypoint.sh

#!/bin/sh
set -e

(
    while inotifywait -qq -e modify /data; 
        do pkill -SIGHUP dnsmasq; # This asks dnsmasq to reload its config.
    done
)&

dnsmasq "$@"

Dockerfile

FROM alpine:edge
RUN apk --no-cache add dnsmasq inotify-tools
COPY ./docker-entrypoint.sh .
VOLUME /data
EXPOSE 53 53/udp
ENTRYPOINT [ "./docker-entrypoint.sh" ]