Burning isn't a big deal with hydrogen balloons. If you look at the Hindenberg fire the skin (cloth with nitrocellulose lacquer) really does the nasty burning. The hydrogen of course burns but fairly slowly and the hydrogen fire goes up into the air quite rapidly - you can't really see this as the actual hydrogen fire is colorless.
For this high altitude gasbag, hydrogen makes a lot of sense. It has more lift than helium for a given size envelope. It's cheap and easy to make from water and electricity and can be liquified relatively easily - helium has to be mined and refined (and the reserves are running out) then stored under extreme pressure as liquifying it takes an enormous amount of energy. for high altitue balloons the gas is contained without any pressure in a limp plastic bag, not a tensioned envelope like a party balloon. At ground level the balloon looks almost empty, at high altitude the pressure is much lower and the gas inside expands to make a more spherical shape. It never goes tight and can't "pop". The primary failure mode for this type of ballon is fairly sedate: the plastic of the bag just tears and the lift gas escapes upwards. I have made a lot of hydrogen lift balloons and tried to light most of them... I'm too cheap to pay for helium but I like sending stuff up in the air. I make the hydrogen either by electrolysis of water or by dissolving aluminum on a strong lye solution, either way gives very wet (humid) hydrogen gas that will lift a lot better after drying. Giant trash bags are the best envelopes I've come up with although a bit too heavy. One bag will lift a kg or so to a decent height but because of the bag weight high altitude is not possible (the reduced amount of hydrogen used to allow room for expansion at altitude is barely enough to lift the bag).
Anyway, lighting the bag full of hydrogen is not hugely different from just tearing it. When you tear one, the gas goes up (invisibly) and the bag flutters down. When you light the bag - just holding a match against the bag works OK - the hydrogen burns quite slowly as it meets air to provide oxygen, the flame front is visible at night but not in daylight. The bag melts around the hole making the hole bigger, the gas goes up relatively invisibly and the bag flutters down.
For this freefall dude, his big risk is that the envelope fails or detaches when the capsule is off the ground but below about 1000 metres - the death zone. There's not enough time to deploy a parachute before crashing below that height although falling from anything more than 10 metres or so will probably be fatal for him. If he has an explosive deployment low altitude safety parachute he might only be in danger below a hundred or so metres. Regardless, hydrogen fire is a tiny risk compared to the others faced. Even on the ground while filling the bag, the fire will go up and he'll be down. Once airborne a fire will be rapidly going up while he rapidly falls down away from it.
Admittedly I've never worked with a gas bag anywhere near this scale, and there might be static electricity issues that make a fire likely if hydrogen is used when you have such a humungous plastig sack flarping around.