I think Kirk understood Burke very well. Both were deeply suspicious of people who think they have the perfect, logical system on which to reorganize society, so neither would have had much truck with today's libertarians ("Complete free trade! It's perfect! Automatically makes everybody richer!" "Open borders...'cause nobody else has a right to tell me where to go" "Legal drugs...'cause nobody has a right...." --you get the idea.) Burke defended institutions which were anything but ideal, like the British monarchy and aristocracy, because he feared radical change and supported institutions which grew organically out of societal history and were supported by custom. Very few people on FR these days seem to understand or support this brand of conservatism.
Since libertarianism is an organizing principle for government, not society, I fail to see the relevance of this observation. (A libertarian society is what arises organically when the government is restrained from interfering -- if anything, it is more, not less, in accordance with Burke's view than a society upon which the conservative version of social engineering is imposed by the state.)