Breeding kings/giants is the same as breeding regular bettas. All the signs of readiness are the same (bubble nest, flirt swimming/dance swimming, etc). If they don't show these signs, I suggest you separate them for a few days.
Try flaring him to another male or mirror - some say for 5 minutes, but I usually do it for a much longer time (up to 1 hour). Put the tanks next to each other with a divider. Lift the divider 1/4 - 1/3 of the tank so they can only see each other at the bottom. If you choose to do this my way, only do it once don't repeat it the next day for the same period of time (they might become stressed if they're not used to it).
IME, after a good sparring match, the male usually will start making a nest. If so, float the female, if they flirt you can release the female or wait a few days before releasing her. All you can do then, is wait and let nature take its course.
I must worn you though, you may not get any kings/giants in F1, specially if the HMPK is regular. You would have to selectively inbreed. As a guide (?) giants can grow to 2cm/>1" in their first 2 weeks, 5cm/2" in 4 months (body only).