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I recall once reading that bleeding the brake system is somewhat different than your typical car.
Can I bring to my mechanic?
Or does it have to be done by a jaguar certified specialist?
If you don't have a vacuum bleeding tool you might need a second person who understands how to step on the brake pedal. But really, no, you can definitely do this at home. If you aren't trying to get air out of the system, you don't have to worry about what corner you do first. Otherwise, bleed the system by going from the furthest corner away to the nearest corner (relative to the master cylinder).
Some people use vacuum bleeders, speed bleed brake nipples, and other stuff but really all that you need is a second person to pump and hold the brakes, brake line wrench, a quart of brand new decent brake fluid, a piece of clear vinyl hose and a pan to drain into. The clear vinyl hose is so that you can see the quality of the fluid (as well as air bubbles), and so you don't spray fluid everywhere.
I really like the Valvoline Dot 3 and 4 fluid for street use, good wet and dry BPs relative to cost, availability and intended purpose. It's under 10$ a quart US and available all over the place.