When you're in the final system, on the beacon map you will see a counter telling you how many jumps you have until the Rebel flagship is in range of the Federation base. This number is measured based on the number of jumps the flagship has left, and the flagship jumps half as fast as you do. That means that you've got around two times the number of jumps shown in order to intercept it. I'd trust this number over any other method of determining it's relative position, personally.
Since each encounter in this system is likely to bring you up against difficult rebel ships with minimal rewards, I don't tend to find it that productive to jump around any more than absolutely unnecessary in order to intercept the flagship.
However, depending on how many jumps you have left and how damaged you are, you may wish to repair between fights. However, a better plan is to avoid damage, either with shields or dodge. Get your engines powered up as far as you can, and/or have a cloaking device to boost your dodge chance. Shields will protect against energy weapons and beams (if they hold out that long...)
Also consider prioritizing damaging the flagship's weapon systems, as that missile launcher especially is killer. The systems are isolated and have just a single crewmember guarding them in the early phases, and the rooms were empty for me during the final fight. A teleporter or missile/bomb launcher can make damaging these systems early in the fight easier.
There's more strategy for beating the boss on this other question.
The flagship doesn't get any easier between fights, so trying to take on the second or third form with a low amount of hull remaining is unlikely to end well. Still, sometimes you've got to play the hand you were dealt...
