Sealed gear with an independent air supply is a must. Depending on the role of these soldiers will change their level of armament. If you wanted they could all be equipped with modern exoskeleton technology. As they are unlikely to be deployed for long periods of time this makes the technology quite viable in this case. Additionally it would allow greater armour capacity,oxygen capacity and allow them to move more freely without tiring from the weight.
A basic level of fireproofing is a must as is heat proofing. This can be achieved through the use of non-flammable coatings and materials,cooled gel layers in the armour supplanted if really necessary by an integral AC unit. Similar to that used in modern Bomb Disposal Suits,Land Warrior and Future Soldier equipment load-outs.
If they are intended to set fires and fight in them I'd recommend starting with napalm airstrikes or white phosphorous artillery bombardment. In a forest or jungle you would spontaneously have a firestorm. Ideal camouflage is a mixture of native forest pattern with accents of black and red. Black for the smoke and ash,red for the raging blaze around them. Add some pieces like used on ghillie suits to break up their outline and make them look like phantoms amidst the smoke and flames.
Weapons wise I'd say that assault rifles,battle rifles,shotguns loaded with slug and HE shells, as well as white phosphorous grenades and grenade launchers would be very effective. The assault rifles and battle rifles providing good firepower,versatility and would be in their effective range within said blaze almost constantly due to the smoke and reduced visibility. The shotguns would be ideal for close quarters engagements and the HE shells serve to further disorient the enemy;additionally they can be used to blast apart barricades and target light vehicles (humvees,technicals,doors,etc). The grenade launchers would provide an easy means of blasting areas with troops sheltering from the blaze (hiding in trenches,bunkers,pill boxes,basements,etc) and the use of fire as a psychological weapon would be extremely effective. Light machine guns would also be ideal for their standard uses within squads for suppression of enemy troops.
For vehicles I'd recommend most MBT's (main battle tanks) with slight modifications where necessary for comfort of troops inside to grant heat protection and prevent smoke from entering inside. You can give the tanks a coaxial flamethrower (as is sometimes done) to make them literally spray fire everywhere as they advance alongside their main gun and turret. APC's for rapid deployment girded up a bit would be nice. But more realistically AFV's (armoured fighting vehicles) would be more useful in a slash and burn operation. Standard air cover can be provided if with reduced visibility,you can fly a drone or two overhead to keep an eye on enemy troop movements to coordinate with ground forces. Making artillery support via mortars brought close to the front easier to manage alongside the firepower of the AFV's and MBT's.
Using weapons that produce fire (white phosphorus,napalm,flamethrowers,incendiary rockets,etc) would add to the horror and confusion. While the solders equipped, (the "Flame Troopers", "Pyroneers", "Grey Devils",whatever name you like);for the inferno would seem monstrous. This can be added too with armour design,decals,the camouflage and also their equipment. If you wanted to be extra cruel they can have specialized recon units that carry camouflaged fire blankets and cover themselves with them in the burning areas. They then would seem to rise from the ashes when attacking enemy troops. Like demons or burning men. Which given the blanket may be on fire,they would very much look like it.
All in all,I found this to be a very interesting idea. Plenty of practical and psychological warfare potential.