Unless a manufacturer has actually specified its use, I don't believe it's advisable to use brake fluid in a hydraulic jack.

Yes, a brake system is a hydraulic system, and brake fluid is a hydraulic fluid - but it's a special hydraulic fluid that carries with it its own baggage as a result of compromises made when formulating it to meet the particular requirements of an automotive braking system. The components of the braking system are designed knowing full well the nature of the fluid, so materials compatibility should not be a problem.

Our hydraulic jacks don't require some of the special characteristics of brake fluid, so we don't need the baggage that comes with it. We can use ordinary (kinder, gentler) hydraulic fluid.

I don't personally know enough about the composition and compatibility of the seals used in hydraulic jacks to make any statement about whether or not brake fluid might be expected to cause damage to the seals. Some of the manufacturers of jacks, however, make if very clear that brake fluid is NOT to be used in their products. This isn't always a case of them pushing their own oil, either. From the documentation that came with my floor jack:(For what it's worth, they also note that, "Pump and cylinder form a closed system and refilling of oil is only necessary in exceptional cases.")

One might also see what one guy who sells and services jacks has to say about it: Otto Service - Jack Basics.