The fact that you have been crew on a commercial(KLM?) airline helps alot but certainly doesn't prepare you for everything that is "private aviation".
I also had 12 years commercial experience but had to adjust to the fact that you duty never really ends....
You'll be most likely be given a phone and that is where work starts and social/private life ends!
Make sure you learn all about food preparation, ingredients, international cuisine, learn how to prepare good food in a very small galley (if not on a heavy jet), talk to other flight attendants, be patient and EXTREMELY flexible.
There is a big difference between flying exclusively for an owner or flying charters.
With an owner you might luck out and end up with a friendly owner , but you can easily be made aware that you are staff and nothing more, depends on the owner/family.
With charters you'll never know what you get, it can be a struggle sometimes regarding ordering catering when brokers want you to get specific stuff that, in the end, the clients didn't even care/ask for!
All in all I would give it a try, see how you like it.
It definately isn't everyones cup of tea and many don't last long for that reason.
Veel plezier!