I don know the amount of increase but it's a really good idea to get max Lvl on your barracks it makes making n army a lot easier for example I can train I infantry In 22 seconds and 1 pony In 51 seconds which compared to lvl 0 barracks is amazing
just work on leveling it up to twenty quickly. its not that resource intensive and timewise its not bad either. the benefit from time saved on troops is huge. its like 1/10th of time from 0 to 20. (5 minutes for a horse compared to 50 seconds)