By "burn rate," I assume, you mean quickness. (Burn rate is a property of the powder substance and varies with the pressure it's burning under -- expressed as so much of an inch per second at such and such a pressure.)
The length of the barrel has nothing whatever to do with either the linear burning rate of the powder substance nor the quickness of its granulation. Let's look at how an expert determines the optimum powder for a brand-new cartridge, which should give you some idea of how powder quickness comes into consideration. Let's say that you (an expert) have created a new cartridge and now want to determine which powder will be its best.
Your first premise is that the powder charge will just fill the case to the base of the bullet (or nearly so -- not less than, say, 90% to 95% of the space behind the seated bullet).
First, you decide on the maximum peak chamber pressure that you want your new cartridge to develop with the one chosen bullet seated to a specified depth -- leaving, IOW, a known space to be filled.
Then the powder to be chosen (or created) is the one that meets both basic criteria -- a caseful of powder that produces no more than the desired maximum peak pressure.
The goal of the handloader is to find the canister powder that exactly or most nearly meets these criteria. Notice that there's no mention of barrel length. Barrel length does not produce or influence peak chamber pressure, therefore does not bear on the optimum burning rate or quickness.
In general, (a) a powder that's slower than the optimum can fill the case 100% and not produce the specified maximum peak pressure, and (b) a powder that's faster than the optimum produces the specified maximum peak pressure with somewhat less than a 100% case fill. The former is safe, the latter dangerously susceptible to overloading.
