I had similar thoughts.
The issue is complicated.
The best stretches are not what we would normally do on the dojo floor.
They might work fine if you started as a toddler, and did them daily for the rest of your life, but they seem less effective as an adult.
So, find a partner, and do "active stretching". There are loads of videos on the web for this sort of thing, and you shouldn't have many problems.
The bigger issue, though, isn't always flexibility... it's a lack of strength in all those ancillary muscles that need to work very hard to lift your leg up higher.
The only answer to that is to actually try and lift your leg up higher, and build up the core strength you need to be able to kick well with your knee pointed higher.
So, to sum up...
If you want to kick higher, you start by kicking higher, and continue to kick a little higher, daily.
There's no magic in Tae Kwon Do; they just make you do it sooner.
Personally, after finding I could kick higher, I still didn't use the kicks all that much.
Truth is, I felt off-balance, and the kick seemed much slower than a nice belly high side kick.
Hope this helps,