Have you been given any advice on sick day rules?
The advice for adults is, if you are ill and have trace ketones give long acting as normal, give usual ratios of fast acting with food and give a fast acting dose which is equivalent to 10% of your total daily dose to get rid of they ketones, keep hydrated and test every 4-6 hours. I have no idea if this applies to children - I'd be calling 111 for advice (or your DSN if you think you will get hold of them at this time on a Friday).
Hopefully a parent will be along to assist, but in the mean time see if you can speak to a real life healthcare professional for proper advice.
Hope he feels better soon.