"To run the gauntlet is to take part in a form of corporal punishment in which the party judged guilty is forced to run between two rows of soldiers, who strike out and attack him." [Wikipedia]
The English word originates from Swedish gatlopp, from gata "lane" and lopp "course, running". The word in English was originally spelled gantelope or gantlope, but soon its pronunciation was influenced by the unrelated word gauntlet (derived from the French gantelet). [Wikipedia]
The Estonian word has the same Swedish origin and, just like its English counterpart, then underwent a popular reinterpretation under the influence of the Estonian lipp. [Eesti etümoloogiasõnaraamat]
Interestingly enough, EKKS signals it as a compound word, "kada|lipp", i.e. slingshot + flag.