That means it's traveling at 1.32 meters per millisecond.
That means an error of 1.32 meters in the length of the tubing would result in a timing error of 1 millisecond.
That means an error of 13.2 centimeters would result in a timing error of 1/10 of one millisecond.
I would think a careful DIYer could probably manage to keep it under a 1.32 centimeter error margin, which would give a timing error of 1/100 of a millisecond.
That being the case, if the speed of the pressure wave is the critical factor, the timing is not a problem.
The next problem to solve is choosing some tubing.  You need to know the pressure of the injection system and then compare that to brake line of the same size.  I would imagine that the size would have to be identical.  It's sure the safe bet, anyway.
I found 
here that NiCopp 3/16 can have a working pressure of 4500 PSI and a burst pressure of 17,900 PSI.
Steel or stainless steel should beat that by a bit, I'm guessing, but I was not able to track down any solid numbers.
So if those pressure numbers work out, you have a solution.
Now the problem of flaring.  For me, I have never been able to use one of those hand flaring tools successfully.  I know many can do great work with them, but I have never gotten the hang of it.
So, when I had a large project to do about 10 years ago, I bought a 
Mastercool hydraulic flaring tool kit for right around $300, and it saved me that much and more in buying lines.  That thing is a BREEZE to use, and gets a perfect flare every time.
I see that that particular model is discontinued now, but I'm sure they have similar.  I also see that 
Eastwood has a similar kit for $360, plus a few Mastercool kits.
They also have 
line bending tools of various kinds.
If it were me, I'd roll my own without a second thought.