Nyasa was already explained here.
The following explanation on Mahanyasa and Laghunyasa can be found here.
FIVE FACES OF SHIVA:-
Because of his five faces Shiva has the name pañcavaktraḥ।
pañcasaṅkhyākāni vaktrāṇi mukhāni nānārūpāṇi yasya sa tathā ।
These faces have the following names. īśāna, ...
The flags of kings, in Ramayana and Mahabharata, were mentioned as having some symbol but not Bhagawa flag.
(i) kovidara (pomegranate) tree was mentioned on the flag of Bharata in Ramayana
एष वै सुमहान् श्रीमान् विटपी सम्प्रकाशते | विराजत्य् उद्गत स्कन्धः
कोविदार ध्वजो रथे || २-९६-१८
"The gigantic and glorious tree with superb branches is ...
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 ...
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, ...