That really depends on the mixture of alkanes you are trying to separate. When molecules are very similar, it is hard to separate them by any means. However, there is quite a bit of difference in polarity on a TLC scale between, say, cyclohexane and n-octane. Normal-phase chromatography, using silica gel and a very non polar eluent like pet ether is probably your best choice.
The worst problem with trying to separate alkanes, especially low molecular weight alkanes, is their volatility. They tend to evaporate off the plate before you can detect them. Stripping the solvent off can also be a major issue, because you strip away the product as well. And since they don't have UV chromaphores or reactive functional groups, detecting them can also be a problem.
Size-exclusion chromatography, as far as I know, is really only useful for macromolecular separations - when you are working with natural polymers (like proteins) or synthetic polymers. I speak under correction here - perhaps someone with more experience on size-exclusion chromatography would like to weigh in? The size difference between a 20 kDa protein and an 18 kDa protein is much more significant on a size exclusion column than the size difference between a sic-carbon alkane and an 8-carbon alkane, regardless of the structure.