How do I find seconds since midnight?

To avoid race conditions, still assuming GNU date:

eval "$(date +'today=%F now=%s')"
midnight=$(date -d "$today 0" +%s)
echo "$((now - midnight))"

With zsh, you can do it internally:

zmodload zsh/datetime
now=$EPOCHSECONDS
strftime -s today %F $now
strftime -rs midnight %F $today
echo $((now - midnight))

Portably, in timezones where there's no daylight saving switch, you could do:

IFS=:
set -- $(date +%T)
echo "$((${1#0} * 3600 + ${2#0} * 60 + ${3#0}))"

The ${X#0} is to strip leading 0s which in some shells like bash, dash and posh cause problems with 09 (where the shell complains about it being an invalid octal number).

There is no need for any arithmetic expression, just use pure date:

date -d "1970-01-01 UTC $(date +%T)" +%s

Based on bash, get current time in milliseconds since midnight, on a GNU system, it can be done like this:

$ now=$(date '+%s')
$ midnight=$(date -d 'today 00:00:00' '+%s')
$ echo $(( now - midnight ))
53983