Yes, you can install a wood-burning stove in a kitchen, but you are likely to need a woodburner with an external air supply
https://www.stovax.com/can-i-have-a-stove-or-fire-in-a-kitchen/
https://salamanderstoves.com/can-you-put-a-small-wood-burning-stove-in-your-kitchen/
Have a look at some inspiration below of our previous installs
and please have a look at the below cook stoves that are superb in a kitchen (or living room), if you click on the Croydon Fireplaces link, you can see the most up to date prices, and also the manufactuers own website where you can view other installations and inspirations.
We have put in Esse Bakeheart
https://www.croydonfireplaces.co.uk/products/stoves/esse-bakeheart-ecodesign-ready
https://www.esse.com/the-ironheart-range/bakeheart/
We have put in Esse Ironheart
https://www.croydonfireplaces.co.uk/products/stoves/esse-ironheart-now-eco-design-ready-model
https://www.esse.com/the-ironheart-range/ironheart-wood-fired-cook-stove/
ESSE wood burning cooker
Stovax Stockton 8
https://www.croydonfireplaces.co.uk/products/stoves/stovax-stockton-8
https://www.stovax.com/stove-fire/stockton-wood-multi-fuel-stoves/stockton-8/
Charnwood Island II
https://www.charnwood.com/all-stoves/room-heating-stoves/island/the-all-new-island-ii/
https://www.croydonfireplaces.co.uk/products/stoves/charnwood-all-new-island-ii
Stuv 30
https://www.croydonfireplaces.co.uk/products/stoves/st%C3%BBv-30-0
https://www.stuv.com/en-gb/wood-burning-stove/stuv-30
If you don't really need the heat, but a focal point then an ecosmart/glammfire bioethanol fire is a great idea.
Please have a look https://local.google.com/place?id=8958282649390841529&use=posts&lpsid=CIHM0ogKEICAgID6zaSkiQE