I don't know about the other schools, but having had experience getting a six-year-old into ESF I can say it wasn't easy.
My husband transferred last October and it has taken us 8 months to secure a place for our daughter.
We put her name down on the nearest ESF school waiting list (Clear Water Bay)as soon as he had sorted an apartment. Although we asked a few times what the wait list was for a place in Year 1, we were only told 'very long'. In short there wasn't a hope of getting a place there. Between July and December you have to apply to your local ESF school (requiring a Hong Kong address before you can apply). From what I was told, all ESF schools will have a waiting list.
From January to June ESF operate a Corporate Surety scheme, which is applied for through your husband's company. If you enter the scheme in January it costs a lot of money (or costs the company if you have that in your relocation deal). but this gets you at the front of the queue for a place at any ESF school. The cost reduces for every month - so if you leave it until June it costs very little to go on the list.
You don't get to choose the school, it is simply done on where the place comes available when you are at the top of the waiting list. So you could end up with a school trip that takes 45mins or an hour +. Or even worse, children at different schools.
After being told that we were 10th on the Surety scheme list in May, we were finally offered a place in mid June for year 2 starting in August, and are now packing up things in the UK to join hubby in HK in 3 weeks
I'm sure there are schools outside of ESF that will be easier to get into, but at a significant cost of course.