HONG KONG
I'll be honest, when it comes to allergy-friendly destinations, I don't think Hong Kong is going to be at the top of the list. It doesn't have the same service culture that Japan has, communication and care-factor in restaurants can be strained at times (i.e. the staff don't always understand the gravity of food allergies or understand the implications of cross-contamination) and some dishes have sauces that could contain seafood (eg oyster sauce), sesame (eg hoisin sauce), peanuts (eg satay - even the dark brown chilli satay sauces that don't look peanut-y), so if anything, staying in accommodation where you can cook meals is quite important in a destination like Hong Kong. We did stay at an airport hotel during our stopover on the way to London (I write about that here) where we ate at the hotel, but during this 5 day trip to Hong Kong, we stayed in an Airbnb. And - it can be done. We even found a goose restaurant that were really accommodating with the allergies!
GETTING THERE
For this trip, we actually flew Qantas as they had a sale when we bought the tickets, and on the way back we travelled in their brand new Dreamliner (789) which made the 10 or so hours pass really quickly! Just little improvements like a bigger bathroom size, an excellent in-flight system (where when you press the screen, it actually does what its meant to do), and compartments for your phone and a USB socket. There are obviously a few options when it comes to airlines flying to Hong Kong, but Qantas have been great lately in terms of being really clear about what is contained in their special meals, so when travelling with food-allergic children, they are a great option. They are also happy to let you board early to wipe down the seats, provided you explain the reason for this at check-in and at the boarding gate (so get to both early!).
WHERE TO STAY
We stayed in Causeway Bay but our decision was mostly influenced by proximity to family, as well as even closer proximity to grocery stores so that we could easily walk to the grocery store if we needed any ingredients. We stayed in an Airbnb just at the back of World Trade Centre; it had a Circle K downstairs and Sogo around the corner and among a bunch of restaurants (we found a goose place (Ki's Roasted Goose) that were pretty good about the nut, sesame, dairy, fish, egg allergies we had to cater for.
PLACES TO VISIT
Our trip was actually cut short for various reasons, but if we had time, we would have taken the kids to Hong Kong Disneyland, Oceanworld, and trip up to the Peak would have been nice too! We've done the latter pre-kids (and seen a bit more of Hong Kong generally, pre-kids) and this trip was mostly to visit family, so while it would have been good to have seen more sights, it just didn't happen for us on this trip, but that's not to say it won't happen for yours!
GROCERY SHOPPING
Hong Kong has quite a few convenience stores around, but we did most of our shopping at Wellcome; there were a couple in Causeway Bay where we were staying; a smaller one near Sogo, and a larger one on Jaffe Road. Both stocked a fair few items that had ingredients listed in English, so this was easier than Japan in that sense. No dairy-free margarine (so we just had to do without!). Fresh produce was easy to buy, so I bought things like salmon and chicken to cook for my kids, and also rice to cook (which I cooked on the stove as the apartment we stayed in did not have a rice-cooker).
OTHER TIPS
Remember to get any necessary vaccines, and also be aware that if any of you or your children have a fever, this is usually picked up at the airport where you are looked at by one of the staff and assessed (for quarantine purposes).
WHERE TO EAT
Our trip was cut short, so we didn't eat out very much (we mostly cooked). There are some delicious bakeries, but these are generally rife with sesame, wheat and dairy, so would not be great options for allergies to these. The mantou steamed buns are fairly common and you can find plain ones that do not to have dairy, nuts or sesame but you still need to be careful as they may be placed next to or amongst other buns with fillings that have sesame (or other allergens); the restaurants we did go to are written about here.