I've got a metal building that I'd like to put a thin brick veneer on. Is it possible to get the thin brick tiles and install over a densglass sheathing?

I'd remove the metal panels on the front and install an exterior rated sheathing, then waterproof and install thinset and brick tiles.

Am I asking for trouble?

Metal buildings usually are not designed to the stiffness required for a rigid covering like brick. My guess is it would start to crack as soon as it was applied.

It can be done. You need to do your research on mortar though. Different mortar types deliver different capabilities when it comes to movement and load bearing ability. They have different tradeoffs, so do some reading and decide what you think you'll need.

You also need to establish what kind of brick you're going to use. There is faux brick that is really more of a manufactured product meant to be attached to a wall face via thinset and lathe as opposed to stacking like a veneer wall. I would not go that route.

Flexing may be less of an issue depending on your anchors. They may allow a certain amount of play that will help minimize cracking.

What is the wall framing comprised of?

No issue installing thin brick on the exterior, provided you use an exterior mortar and grout. You could use densglass and then a sheet good waterproofing made for tile install like Polyguard's Tile Guard or a self-healing fluid applied with lathe.

I came across an interesting support/framing system for thin brick when we started a project with a lot of interior thin brick recently, may be of interest to you: https://brickit.com/systems/systems-dmg

The wall framing is square tubing, but I would probably install some studs on 16" centers in between each column. I would definitely use some sort of exterior rated sheathing like densglass, then use a waterproofer.

Any ideas where to find brick tiles that I can get a few samples of to match to my existing brick?

Best bet is to contact the manufacturer of your current brick. Some of them are making thin brick to match their face brick lines. If you don't know your current brick's manufacturer, check with local masonry supplies that may have supplied your brick.

Absent that, just start googling. The face and thin brick I just used on a project is from https://www.endicott.com/

My house was built in 1974, the current bricks have mexico stamped into them and that is it.

I will start looking around locally to see if I can find anything.