The immediate incentive completely depends on the implementation of Basic Income, and whether parents of children are given a full, partial, or no Basic Income for each child or the first X children, and in a more macroscopic perspective, flies in the face of consistent evidence that educating and bringing families our of poverty is the best way to get them to have fewer children. First of all, most Basic Incomes plans require citizenship as the only condition, but cash transfer programs in developing countries show that immigration to an community receiving cash transfers increases even if immigrants don't receive the transfer themselves, because the program increases the economic activity in the area. I have to say, I think the misaligned incentives would be less warped than the opposite ones that happen today, in which the chronically-ill may have not enough financial support, and the incentive is to cut their life short instead of trying to take care of them. This is in part because an asymmetric difference exists between taking care of one's own day-to-day needs themselves (much harder to do) and willfully taking one's own life (much easier to do) as a chronically sick person. The other way to look at this is that it would act as a subsidy for automation, as labor costs are purposefully pushed up. The immediate effect might seem to be a loss of productivity, but the long term effect might be the acceleration of the development of automation technology, and longer term gains in productivity.This will be a new incentive to have children. I think having children is great, but perhaps we should think twice before giving people who don't want kids a financial reason to.
There will be greater pressure to slow immigration. I believe that immigration is one of the greatest moral and economic wins for the country, and it should be expanded rather than reduced.
There will be greater incentive to keep suffering, terminally-ill people alive longer, making horrific tragedy more likely.
There is no way to avoid the fact that you are reducing the incentive for people to work. Most people work for money. Some people who now work for their basic income will simply stop. Others will work less, or put less effort into finding work, just like many people getting unemployment benefits now. Less work means less production and less wealth to go around.