Busybox doesn't do bash, it only has a minimal sh-like shell. The <() syntax is specific to bash (and some other similar shells). It won't work with POSIX sh or busybox sh or any other minimal shell. That's why you're getting that error.
To get your script to work with busyboxh sh, try:
match=$(echo -n -e '\x38\x6e')match=$'\x38\x63'
for dev in `cat /proc/partitions | $(awk '/[0-9]/{print $4$NF}'`;' /proc/partitions); do
        first=$(head -c 2 /dev/$dev)
        if [ "$first" = "$match" ]
        then
                echo "OK"
                break
        fi
done
 
                