There are several studies looking at this question that give conflicting answers.
Some studies say that the flu shot causes a temporary increase in viral load.
Other studies suggest that it does not. Unless you have very advanced HIV infection, it will probably prevent the flu and all its associated miseries. Some people can develop bacterial pneumonia as a complication of the flu, and people with HIV infection are at greater risk of developing bacterial pneumonia. If the flu shot does increase viral load, it is very temporary, and may not happen at all if you're on effective antiretroviral therapy. For all we know, getting the flu itself may cause a much greater increase in viral load than getting a flu shot.