The external air kit may work OK, but only if the stove is compatible with it. Air under the grate (primary can be from outside), secondary air over the fire is best from inside the room as it is prewarmed.
Stainless twin
wall flue required min 150mm internal diameter and 600 degree temp, 50mm clearance to timber. The ceiling penetration will need to be fire stopped with a special plate that can hold the weight of the flue above the ceiling, then through the roof a roof support bracket is required maintaining 50mm clearance to timber here as well. The minimum flue height is 4.5m, if the roof is tiled then typically the flue has to extend 1m above the surface of the roof, if you are in a windy poistion buy an H terminal or storm cowl. The height above the roof surface can vary depending on the pitch of the roof and the distance from the ridge and other structures. From the stove you can use either twin wall or single skin, some stoves are limited on how much uninsulated pipe you can use. The flue parts must not support the weight of themselves on the stove, so must be bracketed off the wall, either with brackets or a wall plate. If the stoves hearth is deemed less than 100 degrees, then a 12mm overlay hearth can be used, if >100degree hearth then a constructional hearth will be required, details are in Approved Document J. Most stoves with legs have < 100 degree hearths. When reading doc J, it is very confusing and badly written, many people read it incorrectly including installers and manufacturers !!
CO detector is standard fit on these installs. If house is air tight and to latest building spec then 100% of combustion air needs to be provided from outside vent.
Many things to be think about. Twin wall isn't too bad to fit, just bloody expensive, cant be cut, so you have to use adjustable sections which are very expensive. Everyone thinks is is £100/m but you have to add all the brackets and bends and terminal is always seem to come to around £1000 for a average length 5m flue.
If the stove has a fixed flue damper, so if can't be removed easily when you want to sweep it, then you will need a cleaning door on the single skin starter section.
Good luck with the install.
