Though there are few Celtic influences in Dutch history, some words in Scottish accent have striking similarity with Dutch words.
Not to say there is no link between the Netherlands and Scotland; however the perceived similarities between Scots and Dutch can be explained more simply. Both English and Dutch are Low-German Languages (They didn't undergo the same sound shifts as Modern High German) so it stands to reason that there will be some similarity. Following the Norman Invasion, English English replaced some of its Germanic vocabulary with Norman French vocab. Over time pronunciation changed as well. But in Scots and in Northern English dialects, more of the Germanic vocab was retained. Scots also preserved parts of Old English pronunciation: "ch" and "gh" are often pronounced as in German "auch" (a velar fricative). This is of course not to say that Dutch traders, weavers, whoever else, didn't have any contact or impact on Scots. I'm just saying that's not the only reason for the similarity.

Sorry for the rambling, somewhat off-topic proof that I'm a huge linguistics nerd.