But he has never paid a price for his social media tirades, bolstering his reputation as the virtually untouchable successor to one of Africa's longest-serving rulers, experts say.
And capping a meteoric rise, the government announced late Thursday that Museveni has appointed his only son to head Uganda's defence forces.
The 49-year-old, known as Muhoozi, first came to wider attention in 1998.
Then a fresh-faced graduate, he began recruiting students for the presidential guard, raising questions about whether his father was trying to build a political dynasty.
Museveni brushed off the speculation but Kainerugaba rose swiftly through Ugandan army ranks, training at Britain's elite military academy Sandhurst, as well as in Egypt, the United States and South Africa.
"With senior command courses lined up, one after another, promotions after another, it was clear Muhoozi was being prepared for higher positions in the military," Kampala-based security analyst Lauben Oketch told AFP last year.
Kainerugaba was sent on senior command courses above his rank "to accelerate his promotions and the family agenda", he added.
- 'Enough of the old people' -
His dizzying career trajectory saw him promoted to brigadier and put in charge of Uganda's all-powerful Special Forces Command, before his elevation to major general in 2016, and now defence forces chief.
He was deployed in South Sudan and Somalia as part of Ugandan interventions to shore up governments there and played a prominent role in campaigns against the notorious Lord's Resistance Army (LRA) and the Allied Democratic Forces (ADF) militia.
In March last year, Kainerugaba announced plans to run for the presidency in 2026 in a social media post that was later deleted.
He also appeared to take a dig at his father, writing: "Enough of the old people ruling us. Dominating us. It's time for our generation to shine."
Mwambutsya Ndebesa, an academic at Makerere University in Kampala, told AFP the comments were possibly "intended to be a smokescreen, a resemblance of internal democracy and free expression within the ruling class, which in reality is not the case".
To many Ugandans, Kainerugaba's position as heir apparent is obvious, but the government has taken a harsh line against anyone discussing the matter.
In 2013, police shut four media outlets for 10 days after they published a leaked confidential memo by a senior general alleging that Museveni was grooming Kainerugaba to succeed him.
The general -- former intelligence chief David Sejusa -- fled to Britain and said anyone opposed to the so-called "Muhoozi project" risked being assassinated.
Many of Museveni's former allies, including his personal doctor Kizza Besigye, have fallen out of favour with the president over Kainerugaba's elevation, which has also aroused the ire of government critics.
- 'Baby despot' -
Prominent author Kakwenza Rukirabashaija fled to Germany in 2022, alleging he was tortured in custody on charges of insulting Museveni and Kainerugaba, who he has described as "obese", a "curmudgeon" and a "baby despot".
As presidential adviser, Kainerugaba's online commentary on sensitive foreign policy matters has often created headaches for the government.
After he threatened in 2022 to "capture Nairobi", a red-faced Museveni was forced to apologise to Kenya and tell his wayward son to stop discussing affairs of state on social media.
At the time, 79-year-old leader also relieved his son of the command of Uganda's land forces even as he promoted him to the rank of general.
Kainerugaba remains a polarising figure, feared by many, but also praised for philanthropic acts, such as paying students' medical costs or footing the hotel bill for the cash-strapped national basketball team during the 2021 AfroBasket championships.
Married to Charlotte, a businesswoman, the father-of-three is said to have been instrumental in a rapprochement between Uganda and Rwanda in 2022.
He was also rumoured to have played a key role in a joint operation by Ugandan and Congolese forces in 2021 against the ADF in the eastern DR Congo.
To many Ugandans, his succession is a foregone conclusion engineered by his father.
"Museveni is very calculative. He doesn't want the public to know he is behind his son's political ambitions," said Ndebesa.
"He prefers to keep the population guessing even when it's clear to many of us that he wants him to take over the mantle when he leaves power."
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