..Since it sounds like you haven't bought any of the towing hardware yet, I highly, HIGHLY recommend you look at the tow bar and integrated braking system offered by NSA, the
Readybrute Elite tow bar and Readybrake braking system package.
You basically get a very nice tow bar AND braking system, for almost the same $$ as you'll pay for just a tow bar alone from anyone else. That alone right there, will save you several hundred $$ (close to $1k) from what you'll pay for a tow bar and separate braking system of any other type. And, you get a very simple, reliable, no-nonsense cable operated braking sytem that simply works, and works great.
As to your specific question about installation cost for a braking system: Really depends a lot on the braking system and the vehicle involved. Can range anywhere from $0 for a 'brake-in-a-box' system like Brake Buddy that you have to put in and take out every time you tow, to right up around $1000 for installation of the more complicated electronic systems.
The Readybrake system I mentioned is somewhere between those two extremes, again depending on the vehicle involved. It is a pretty simple installation, though, since it only involves installing, routing a physical cable from the brake pedal out to front of the vehicle.
A good point was made earlier, too: Are you asking about strictly the cost of installation with regards to a braking system, or installation of everything required for flat towing? There is a huge difference, as there are other installation costs for flat towing that you have to do regardless whether you use a braking system or not: Base plates, tail light wiring, etc.
Will and Cheryl
2021 Newmar Baystar 3014 on F53 (7.3 V8) Chassis ("Brook")
2018 Jeep Wrangler JK ("Wilbur")