In one of his comments, Dan suggested that words such as brdar, bdar, and gdar (only in the sense of rectangular shape?) could have something to do with dar. Let us take a look at these words and speculate. It turns out that there are several such words that are either homophones, homonyms, or, homographs.
(a) First, bdar or brdar in phyi bdar/brdar byed pa (Jäschke 1881: s.v.) or phyag bdar/brdar byed pa (“to clean/cleanse”) actually seems to mean “polish” or “sweep.” The word phyi bdar/brdar itself contains two quasi-synonymous components “wipe” and “polish.” In the famous expression bsregs bcad brdar ba’i gser bzhin du, brdar again means “to rasp,” “to rub,” “to polish.” By the way, also star ba seems to have cognates with bdar/brdar ba. Note also so brdar ba “to gnash/grind [one’s] teeth.” This is also true in in zhib tu rdar ba “to grind thoroughly” or phye mar bdar ba “to grind to powder,” “to pulverise.” The question is whether dar (substantive) “silk” has anything to do with bdar/brdar ba in the sense of “to polish,” “to file,” and by extension “to smoothen,” “to refine,” “to hone.” One can imagine a connection between the two inasmuch as “silk” is obtained through a special process of “refinement.” And dar in the sense of “cloth” or “flag” maybe related to dar in the sense of “silk”? Perhaps in Tibetan language, one can imagine several kinds of refinement such refining grains to obtain fine tsam pa; refining silk-cocoons so as to obtain fine silk-threads; refining gold-ore so as to obtain pure gold; and perhaps even refining liquids such as fermented milk so as to obtain “butter-milk” (dar ba, but in some Bhutanese languages one might spell as star). By the way, Jäschke puts a question mark to dar tshil “groin”? But I wonder if dar tshil is (as in rDzong-kha) “cheese” and hence literally “fat/essence of mutter-milk.”
(b) The next question is if the heteronomous-intransitive verb 'dar ba (“to shiver” or “to tremble”) has anything to do with our autonomous-transitive verb bdar/brdar ba “to file/polish.” The “act of rubbing/filing” and the “event of shivering/trembling” are somehow related? At any rate, sdar ma (“trembling, timid,” “coward”) seems related to 'dar ba. Perhaps dar tsam and dar gcig, too, are related with “quiver,” that “a slight tremble” is somehow indicative of “one moment” or a “short span of time.”
(c) Third, what about dar ba (“to be diffused,” “to spread,” “to flourish”)? I cannot see how this would be related with our above bdar/brdar ba and ’dar ba. But dar mo (“prime of life” or “person in the prime of life“ as in dar po and dar mo) is obviously related with dar ba. Perhaps dar in the sense of “flag” is related to “silk/cloth” although it would also make sense to link it with “to flutter” and “to flourish.”
My goodness, all of these are very uncertain!