The study of flags is called vexillology - from the Latin - "vexillum" - which was the metal standard - (often, the eagle) - that Roman armies carried as they advanced into battle.
The word may not be in some of your dictionaries - as it was only introduced into the English language in 1956 - in an article by Witney Smith in the Flag Bulletin. (USA).
Vexillography is the art of designing flags.

The British Naval Ensign is constructed as a Union Jack in the canton, on a blue "field". As the British Empire grew, the British Admirality allowed the British Naval Ensign to be "defaced" - the correct heraldic term - by a symbolic representation of the colony, protectorate or dependency.
In the case of the Union of Ionian States, this was the winged lion of St Marcus.
In the case of Australia - the "defacement" is the single Commonwealth Star, and the 5 stars of the Southern Cross, on the "fly". The "fly" is the less consequential part of a canton-based flag to the viewers right.




Image by Antonio Martins.

From:

http://www.nationalflaggen.de/flags-of-the-world/flags/gr-ion.html#bri

"From 1815 to 1864 the Ionian Islands were under the protection of England and were called the "Union of the Ionian Islands". The flag with the Venetian Lion was again in use after 1817, with the addition of the British flag on the upper corner".

The following is an extract from A Constitutional Chart of the United States of the Ionian Islands, as reproduced in an appendix to R.M.Martin's History of the Colonies of the British Empire (1834).

"Ratified by HRH the Prince Regent, in the name and on the behalf of His Majesty 26th August 1817.

Chapter VII Miscellaneous.

Section VI. Of the National Colours and Armorial Bearings.

Article 1. The national commercial flag of the United States of the Ionian Islands, as directed by the seventh article of the treaty of Paris, shall be the original flag of these States, with the addition of the British Union, to be placed in the upper corner, next to the flag-staff.

Article 2. On usual days, the British colours shall be hoisted on all the forts within the United States of the Ionian Islands, but a standard shall be made, to be hoisted on days of public rejoicing and festivity, according to the model of the armorial bearings of the said States.

Article 3. The arms or armorial bearings of the United States of the Ionian Islands shall hereafter consist of the British arms in the centre, surrounded by the arms of each of the islands composing the said States.

Article 4. The armorial bearings of each of the islands shall consist of the individual arms of the islands, and such emblem, denoting the sovereign protection, as may be deemed advisable."



George C Poulos

Executive Director, Australian Iconography Foundation
Senior Member, Flag Society of Australia
Member, Heraldry Australia Inc.
Vexillographer, Official Bondi Beach Flag.
Vexillographer, Hawkesbury Waratah Festival Flag.
Vexillographer, Karavitiko Symposium Flag.
Vexillographer, Australian Total Reconciliation Flag.