Hi I live in Allschwil and my 9 year old son is in the local primary school. There are quite a few English speaking/German speaking kids I know who attend the local primary school and Kindergarten here.
I can only speak from my own experience - but I've been very happy so far with the Kindergarten (which was in fact quite exceptional - my son went to the one attached to the primary school here) and also with the school.
I'm a teacher myself so I speak from that perspective.
If you move here now your son will have to go into the 2nd year at Kindergarten - but actually this would probably be very good for him - they focus mainly on discovering nature (my son's Kindergarten went to the forest or out every week for 2 years) and social skills/learning through play. They also have intensive German support for non-German speaking kids at Kindergarten. One of my sons friends is from Sri Lanka and he couldn't really speak German in Kinski - but now he's doing very well in primary school.
The primary system they have special German intensive courses for children arriving from other countries and these work very well. A case I can give is, a Polish boy arrived into my sons class this year - he didn't speak a word of German - it's taken a few months but slowly he's getting there and integrating. This is something the schools are quite used to working with.
Regarding English - in Allschwil the first foreign language is in fact French not English. The kids start with that in the 4th class at primary school - so from age 10.
I'd strongly advise enrolling both your kids in the Open Door which is an English afternoon school in Basel.
http://www.opendoorbasel.ch/index.html
My son has been going since the age of 2. The older kids go every Wednesday afternoon for a few hours (when there is no Swiss School) and learn to read and write in English. It's excellent and they follow the primary school syllabus from the UK.
Feel free to pm me if you have more questions.
Best Wishes
Steph