I grew them many years ago on clay. No trouble. Don't remember doing anything special.
It was very very popular in the 1960s. As I recall it was only half hardy in South Yorkshire. Very pretty.
You make me feel old pansy, I grew it in the 70s as an annual.
I have bought the seeds bu haven't sown yet. I don't think they are a bother at all, I remember them when I was a child, they are only annuals.
I also grew them a long time ago, can't quite remember when but I don't think they were any trouble to grow. As Lyn and B3 said, they were were popular and were often grown in bedding displays with other annuals. I have checked a book on growing from seed and it says they are a hardy annual "germinate them at 15-20 in March - April. Germination 5-7 days. Prick out and grow on and plant out in May. It grows best in a sunny position".
Hope you have some luck with them.
DL It's March 1st on Tuesday so it sounds as though your Kochia will be raring to go down there in sunny old Costa del Newport. Hope they grow well for you. It's bright and sunny but still cold here.
They're might be too wet, I haven't grown these but most things like a watering when they need it then dry out a bit. Constantly wet leaves sounds a recipe for fungal attack