I hope that the excellent NHS staff can get you all sorted and back on track soon with a full recovery for your son, and that BA take care of everything.

Whilst not an excuse for possibly tardy/lacklustre first aid/assistance, the first step to dealing with an incident is always "danger"....is there any? I imagine split liquids need to be dealt with ASAP to prevent further incidents, and that might have been the first thing on the lounge staff's mind.

I don't know if the kitchen staff have any First Aid training (i'd guess most don't, but there should always be someone on hand that is first aid trained), and that they'd not want to become too involved medically if they didn't have a clue what they were doing (which is a good thing - bad medical intervention is worse than no medical intervention, especially with burns). In retrospect the staff involved will probably think "oh, I should have done XYZ", but that's something that can only come from experience, especially if there is no mandatory first aid training. If this had happened onboard, all crew are first aid trained, so would have been more adept at assisting you.