In particular, the timeline claims that in 1997, after an alleged National Prayer & Repentance Campaign, the President of the Republic at the time, Yoweri Museveni, handed the national flag to intercessors (with the implied purpose of praying for the nation).
In an attempt to cross-check the claim with other sources, I came across other sites making complementary claims. For example, this site talks about an alleged Revival in Uganda, and claims:
On New Year's Eve, 1999, President and first lady Museveni joined a huge stadium celebration where a public proclamation was read in which they covenanted with God for the land of Uganda to be used for the next 1,000 years for the purposes of God and the Lordship of Jesus Christ.
Similarly, this site claims:
New covenant with the living God
President Museveni repealed Amin's Islamic covenant, and gave the national flag to a group of intercessors as a prophetic symbol during a conference, re-dedicating the nation to the God of the Bible. That broke the dam.
And this one, although it disagrees on the date, makes a similar claim:
From this prophecy the Mulinde-led National Prayer and Fasting Campaign was born. The main focus of this movement, aimed at "praying into place God's principles of nation-building," has been the AfriCamp, a massive prayer rally held annually and usually attended by the president.
As a result, all of Uganda joins in prayer and fasting at the beginning of every year, meeting in public places around the country and standing against the dark forces arrayed against the nation. In 2000, the people and the president, who was flanked by his entire cabinet, made a covenant with God to renounce idolatry and witchcraft. The president handed over the national flag to the assembled ministers, symbolically turning the nation over to God.
Did Uganda's president Yoweri Museveni hand the national flag to intercessors?