Eh, I'm not really convinced here that the Catachan's have enough superiority over the RDA to have a dramatically better chance, and if they have to move by foot, potentially significantly worse. People forget how much slower by foot can be. Even one hour of helicopter travel is 200-300 km. That's roughly 10-30 days on foot, with good conditions. The faster speeds requiring traveling lighter, which makes them more vulnerable to to arrow and skirmishing.
Burning through requires constant resupply: flamethowers are, well, not particularly ammo efficient: quick google suggests WWII back pack ones had about 10 seconds of flaming. The Churchill Crocodile got 80 seconds of flaming out of 400 gallons of fuel, roughly 1.2 tons of fuel. A battalion looking at the force structure has something like 4-8 Hellhounds.
Promethium seems to just be a generic word for hydrocarbon fuel, so it might be marginally better, but I'm not sure an order of magnitude better than conventional flamethrowers.
Still, keeping those 8 flame tanks in fuel to burn through the forest is maybe 50-100 tons of fuel per day on a conservative side? Roughly 30,000 gallons of flame fuel per day? Conventional off road fuel trucks have about
3,000 gallon capacity. So, this 800 man group needs 10 fuel trucks just on flamer fuel. 20 overall Bradley scale vehicles is maybe 200 gal each, maybe 4,000 gallon of fuel? Bradley nominally has 400 km of range, so theoretically not a huge need of fuel, but combat can also make the practical range on a tank much lower.
So, even this force potentially has a fairly extensive logistic trail, which would be very venerable to guerilla and harassing. And the slow and methodical is also going to burn through immense amounts of material, which may not be easy to replace, and is another target of attrition.
The Catachan force present here might be less qualified for the mission than the RHA.