Can you adapt something like this
v=Map[Point,Table[RandomReal[{0,1},3],{20}]];
Animate[Graphics3D[Take[v,i],PlotRange->{{0,1},{0,1},{0,1}}],{i,1,Length[v],1},
AnimationRate->1,RefreshRate->1/4]
The Table in the first line is creating 20 rows of 3 columns, replace that with your actual data.
The Map Point in the first line is wrapping Point around each of your rows.
The Animate is displaying a slide show with each slide taking one more Point from your Table. You will need to adjust the PlotRange to reflect the range of your data points. You can adjust the AnimationRate and RefreshRate once you see how your data looks.
I did approximately the same thing using ListPointPlot3D, discarding the Map Point and Graphics3D, and the results were similar.