How can I put thin brick/veneer around my fireplace?

You can get veneer brick. I recently saw someone use it on their kitchen backsplash and it looked beautiful.

Get yourself some tile glue tell the employee your putting it on a fireplace so he gives you the right product start around the fireplace it self work out to edges finish with a wood trim on top or mantle.

There is a product called air stone that will be perfect for what you want. If you Google air stone, you'll probably get a link to the Hometalk project that was done recently. Looks fabulous and is fairly easy.

It should look OK using the veneer.

How far forward does the fireplace extend (the brass part)? Take that into consideration as putting veneer on the wall will not look right if it sticks out too far. I would also spray the brass black prior to beginning.

If the fire box is flush to the wall, you may want to consider a brick look textured wallpaper that you can then paint/German smear, etc. for the look you want. The cost will be far less than a veneer and installation is much easier. Another plus to doing this is that you can easily remove it if you want to change the look in the future.

Here are pics and examples

https://www.amazon.com/Wallpaper-Removable-Waterproof-Livingroom-Decoration/dp/B077WQ6NNT

https://www.wayfair.com/decor-pillows/sb1/brick-wood-stone-wallpaper-c1861000-a85976~302511.html

https://www.amazon.com/slp/faux-brick-wallpaper/dscpc4wkdqds4zr

Another option are faux brick panels that glue on and are easily cut. They are about 1/4" thick. Here are pics and examples

https://www.fauxpanels.com/portfolio.php?gclid=CjwKCAjwpuXpBRAAEiwAyRRPgeD0LA3pIhPzZ9XpXccoB-nTdc_0khyAb5Hku-8AdFYBLu6PDkoomhoCdXMQAvD_BwE

https://www.flooranddecor.com/ledgers-stone?keyword=faux%20brick%20wall%20tiles&gclid=CjwKCAjwpuXpBRAAEiwAyRRPgdLUyyA2Xf43AhmgYyfz6S9_zZwrMJzV899TNVuHeU2MGgOnw-3ODRoCwS0QAvD_BwE

https://www.textureplus.com/store/faux-brick-paneling.html

https://www.hometalk.com/diy/decorate/walls/how-to-build-an-interior-reclaimed-brick-veneer-wall-27664345

https://www.hometalk.com/diy/decorate/walls/real-thin-brick-accent-wall-34381718

Use manufacturers recommended fiixing or ask at DIY store for help. You could ofcourse use Board that is made to look like a brickwall or maybe wallpaper. They make some good ones now. Failing that, cut a spong into a brick shape and dip that into paint and make your own brick wall, leaving the background colour inbetween to be your mortar line. Have fun!