Brindle coat markings are attributed to the brindle gene. This is relatively common in the animal kingdom affecting not only dogs but also cats and even horses.
However, when it comes to dogs, few breeds are affected in which case the dachshund is one of the most common dogs you will find the gene in.
The brindle gene is a dominant variant. Without turning this into a whole science class on genetics, let us simply say this makes it easier to pass down.
This is because only one parent has to have the gene for it to appear in the doxie pup. So if you breed a brindle dachshund with a regular one there will be brindles in the litter.
With this logic in mind, brindle dachshunds are technically not very rare.
This is in comparison to piebalds where you have to breed two piebalds or 2 carriers of the gene specifically to get them. With brindles, the pattern of passing down the gene makes them easier to come by and as a result among the most common variant coat patterns in the dachshund breed.
However, without comparing them to other dachshund coat markings (there are 25 of them as far as we know), brindles are relatively rare.
This is because normal coat doxies are typically easier to come by and more commonly bred. With brindles on the other hand, breeding is more often than not intentional to produce the unique dog.
In a nutshell, do not fall for the hype of shady breeders who mark up these dogs with the claims that they are super rare. The truth is that though they are not the most common type of doxie, they are considerably common so all you have to do is take your search elsewhere. You might even find one in a rescue shelter for free.