Visa on Arrival to Shenzhen but I fly home from HK

Actually, there are several eligible entry/exit points for Shenzhen VOA, so you are perfectly eligible for obtaining one upon your arrival at Shenzhen airport and after that to cross the border to Hong Kong. However, it is highly advisable to bring with you your flight ticket from Hong Kong to some other country and also your accommodation booking confirmation in hard copy.

Yes, this is perfectly allowed. You will arrive at Shenzhen airport where you will apply for Shenzhen VOA. It is advisable to have your accommodation booking in hard copy for the time you plan to spend in Shenzhen. After you have received your VOA you will stay in Shenzhen for up to 5 days and when you decide, you will just take a bus or train or local transport or whatever and travel to Hong Kong.

The alternative to this option, and I would definitely recommend it, is 144 hours visa free transit. I assume that you will arrive to Shenzhen from some other country different than mainland China. If so, you will just have to buy your ferry ticket from Shenzhen Shekou port to Hong Kong online in advance because this is the condition to have an evidence that you will travel from country A to country B (mainland China) to country C (Hong Kong, although not a country is considered as third country in this regard). So, the advantage of 144 hours is the possibility of moving not just within Shenzhen Special Economic Area, but also within the entire Guangdong province. Also, this option is free from any charge.

Of course, 144 hours visa free transit has one drawback compared to Shenzhen VOA and that is the fact that you have to decide and stick to that decision to travel with the ferry you have bought your ticket for. So, this option does not give you any autonomy when and where you will travel to Hong Kong.

OK, now when you know the options, you can make a decision for yourself.

Yes, this is perfectly allowed. You will arrive at Shenzhen airport where you will apply for Shenzhen VOA. It is advisable to have your accommodation booking in hard copy for the time you plan to spend in Shenzhen. After you have received your VOA you will stay in Shenzhen for up to 5 days and when you decide, you will just take a bus or train or local transport or whatever and travel to Hong Kong.

The alternative to this option, and I would definitely recommend it, is 144 hours visa free transit. I assume that you will arrive to Shenzhen from some other country different than mainland China. If so, you will just have to buy your ferry ticket from Shenzhen Shekou port to Hong Kong online in advance because this is the condition to have an evidence that you will travel from country A to country B (mainland China) to country C (Hong Kong, although not a country is considered as third country in this regard). So, the advantage of 144 hours is the possibility of moving not just within Shenzhen Special Economic Area, but also within the entire Guangdong province. Also, this option is free from any charge.

Of course, 144 hours visa free transit has one drawback compared to Shenzhen VOA and that is the fact that you have to decide and stick to that decision to travel with the ferry you have bought your ticket for. So, this option does not give you any autonomy when and where you will travel to Hong Kong.