I found in a catalogue a low-quality, black-and-white image of a postage stamp sheet released by Venezuela on 3 July 2005. The sheet is captioned (on the catalogue) "Latin-American Parliament". The writings on the sheet borders and on the stamps are not legible on the catalogue. One of the stamp shows a flag with an emblem, itself detailed on an other stamp. The emblem shows a map of Latin America, apparently including Central America and the Caribbean Islands, surrounded by a wreath.
It appears to be the flag shown in the third photo to the right of the Andean Community flag. The field is light blue, with the emblem green on white. The website of the Parliament shows that emblem, but I could not find an image of the flag.
A brief description of the Parliament is given, translated--poorly--by yours truly:
On the 7th of December of 1964 in the city of Lima, after a struggle dating back a full half-century, the Latin American Parliament was constituted. According to one of the paragraphs of the Declaration of Lima, it exists as a permanent democratic institution, representative of all the existing political tendencies in our legislative bodies; and to promote, to harmonize and channel movement towards integration.
The Latin American Parliament (Parlatino), is a regional, permanent and unicameral organism, integrated by the national Parliaments of Latin America, elected democratically by means of popular suffrage in countries that ratified the corresponding Treaty of Institutionalization signed on the 16th of November, 1987, in Lima, Peru, and those whose States adhered to the treaty at a later time, in accordance with the procedures indicated in this Statute. The admission of other members is the exclusive prerogative of the Assembly.
The Parliament has the following permanent and unalterable principles:
The defense of democracy
The self-determination of peoples
The political and ideological plurality as a basis of a democratically organized Latin American community
The legal equality of the States
To condemn the threat and the use of force against political independence and the territorial integrity of any State
The peaceful, just and negotiated settlement of international disputes
The promotion of principles of international law in to further friendly and cooperative relations between the States.
The members of Parlatino are: