In I want to introduce my own country in Japanese! (1) we looked at...
・a site called 世界の国旗 (National Flags of the World), which includes some basic information on different countries along with their national flags,

世界の国旗 (National Flags of the World)

Let's look at a few more interesting sites concerned with country names and flags.
These are Japanese-language only sites, so you could either use reading tools such as the ones above, or if you are an advanced learner you might enjoy making use of this opportunity to test your skills...

国旗クイズ (National Flag Quiz)

There are quizzes about world flags here, which could make a good starting point for a speech.
How many of the quizzes can you do?
(These contents are part of 世界の国旗 [World Flags])

Aside from some basic facts about different countries, here you can also gather some information on national flags and their origins.

南アジア各国の国旗の意味 (The Meanings of the Flags of Each Southern Asian Country)

Here you can find out about India, Sri Lanka, Nepal, Pakistan, Bangladesh, Bhutan and the Maldives.
(These contents are part of Center for South Asia Studies (CSAS), Gifu Wome's University)

世界の国旗図鑑 (Illustrated Reference Book on World Flags)

On this site, aside from the flag's meaning and origins, you can also find interesting contents such as maps showing each country's position, an aspect ratio of the flags, information on the correct etiquette for hoisting and lowering flags, a section called 世界の国旗占い (World flag fortune-telling) and more. (These contents are part of Sarago, Inc.)

Information on Cambodia

地図 (Maps)

We tried the 世界の国旗占い (World flag fortune-telling). Tomorrow's horoscope was "Angola", apparently.
Here you can find out business fortune, economic fortune, and your luck in love and health.