Welcome to the Forum, and I am sorry to hear about your family problems.
You can apply for immediate testing, but you need to provide confirmation
of your house move in order to apply. Effectively that means that you must be committed to moving, but the test can be taken before you physically move to Bucks.
The information you need is on pp 23 & 24 of the PDF "Guide for Parents - Secondary" on this link.
The catchment schools for boys in Chesham are Chesham High School (mixed) and Dr Challoners GS (boys only). If he qualifies for the Bucks 11+ you should be able to secure a place at CHS, but you would need to go to a Transfer Appeal for DCGS, because there is still a waiting list for Year 7. Transfer appeals for DCGS are very rarely successful anyway.
I have sent you a PM.