Chimney draught excluders are available from most diy stores.
Hinged flap door draught excluder.
So to get round this you could install a hinged type instead.
The main reason being is that the moment the cat flap is opened it has created a draught hence no cat flap manufacturer can claim that it is draught proof.
One of the main problems with the simple flat excluders is that they drag across the floor when the door is opened.
Fit brush or hinged flap draught excluders fitted along the bottom of the doors see below interior doors.
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Cut draughts with snake draught excluders photo right brushes or similar strips of material see below unused chimneys.
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Doors can be insulated either by attaching excluders to the door itself or sticking them on the frame and all sorts of windows including hinged sash and sliding doors can be insulated using easyfix draught excluders.
A wide selection of letterbox excluders are also detailed.
However instead of brushes this method relies on a flexible strip to prevent draughts.
The only way you could avoid this would be like a hotel revolving door that never actually opens as such you enter a compartment that then moves around to the opening so you can get out.
Where a door has a high sill you ll have to use a type that closes against the sill itself rather than rests on the floor.