It's simple math:

for i in $(seq 10); do
  ffmpeg -i video.mp4 -ss $((i%3600):$((i/60%60)):$((i%60)) -t 00:10:00 -c copy ${i}.mp4
done

If you want to have leading zeroes in the file name:

for i in $(seq 10); do
  name=$((i+100)); name=${name#1}
  ffmpeg -i video.mp4 -ss $((i%3600):$((i/60%60)):$((i%60)) -t 00:10:00 -c copy $name.mp4
done

It's simple math: the hour figure is $((i%3600), the minutes are $((i/60%60)), the seconds are $((i%60)). To add a leading zero where needed, a simple trick is to add 100, then strip the leading 1. Do the same with the file name if you want to avoid leading zeroes.

for i in $(seq 10); do
  minutes=$((i / 60 % 60 + 100)); minutes=${minutes#1}
  seconds=$((i%60)); seconds=${seconds#1}
  i=$((i+100)); i=${i#1}
  ffmpeg -i video.mp4 -ss $((i%3600):$minutes:$seconds -t 00:10:00 -c copy ${i}.mp4
done