Modern Hindu organisations usually use saffron triangular flag as a unanimously accepted symbol of Hinduism. However, does the flag or colour have any significance as per authentic Hindu scriptures?
Not sure about flag, but the color sure have important place in Sanatana Dharma. All Rishis/Munis used to wear yellowish color'ed clothes which is nearly same as Saffron color. Here is a reference from Rigveda Suktam 10 Hymn 136:
मुनयो वातरशनाः पिशङ्गा वसते मला ।
वातस्यानु ध्राजिं यन्ति यद्देवासो अविक्षत ॥२॥
The Munis, girdled with the wind, wear garments soiled of yellow hue. They, following the wind's swift course go where the Gods have gone before.
Note: The reference to this hymn I found from wikipedia article on Sannyasa. As per my understanding from the article, It seems the English word for "soiled of yellow hue" is Saffron. That is why they referred that as Saffron when mentioning the short translation of that hymn. Hence I put Saffron in bracket since there is no direct mentioning of the word in the book but it was Wikipedia all alone.
The Ochre color, which is very close to Saffron, has been prescribed as the color of an ascetic's garments.
6 A wandering ascetic should wander forth according to the rule, abandoning his relatives and free of possessions. 17 Going into the wilderness, 18 he has his head shaven except for the topknot; 19 wears a loin cloth; 20 resides in one place during the rainy season ; 21 and wears ochre clothes
Baudhayana Dharma Sutras 184.108.40.206-21
There can be similar verses in other scriptures as well and such verses must be the reason why the saffron/ochre color gradually got associated with the Hindu Sannyasis (ascetics). Not sure though about the reasons for flags to be of a particular design.
However, note that it is forbidden to perform Vedic rituals etc dressed in garments of that color.
When someone engages in the soft recitation of prayers, performs a sacrifice, or accepts a gift dressed in ochre clothes––an oblation made in this way at a rite to gods or ancestors does not reach its deity.
Baudhayana Dharma Sutras 2.15.5
But then again you have to understand that saffron/ochre is mostly associated with Sannyasis and the Sannyasis abandon fire sacrifice, Vedic rituals among many other things.