From
Wikipedia:
The flag of Switzerland
consists of a red flag with a bold, equilateral white cross
in the center.
The ultimate origin of the white cross is attributed by
three competing legends: To the Theban Legion, to the
Reichssturmfahne attested from the 12th century, and to the
Arma Christi that were especially venerated in the three
forest cantons, and which they were allegedly allowed to
display on the formerly uniformly red battle flag from 1289
by king Rudolph I of Habsburg at the occasion of a campaign
to Besançon.
The oldest surviving specimen of a flag of Schwyz dates to
the Burgundian Wars (1474–77). The illustrated chronicles
show an asymmetrical white cross, drawn in greater detail,
including the body of Christ, and the equilateral cross
became predominant only in the later 17th century.
Use of a white cross as a mark of identification of the
combined troops of the Old Swiss Confederacy is first
attested in the Battle of Laupen (1339), where it was sewn
on combatants' clothing as two stripes of textile,
contrasting with the red St. George's cross of Habsburg
Austria, and with the St. Andrew's cross used by Burgundy
and Maximilian I.
Civilian use of the white cross as a symbol of the
confederacy is attested from the 16th century. From the 17th
century, the white cross was carried on the banners of all
cantonal troops, on the background of the cantonal colours.
General Niklaus Franz von Bachmann used the white cross in a
red field in 1800 and 1815, and following this use, the
symbol was adopted as national symbol in the federal
contract of 1815 (see also Switzerland in the Napoleonic
era).
General Guillaume-Henri Dufour proposed use of the flag for
the federal forces in 1840, and in 1889 the Federal Council
defined the 1/6th proportion of the cross's members, while
the ratio of the cross to the square field, or the shield in
the case of the coat of arms, remained unspecified.