With FDM printing, integrating colors into complex shapes is a challenge. You can either design your parts to be printed in individual colors and then assembled (this is tricky when it comes to interlocking parts like a barber's pole) Or you can switch colors while printing the layer (which is very time consuming, and if you only have one extruder, it tends to waste a lot of filament)
I'm not familiar with TinkerCAD and its toolset. I personally do this in my slicer. I use OrcaSlicer (which is a derivative of BambuSlicer, which is a derivative of PrusaSlicer) which has a paint mode where you can define which colors to use where. You can paint by a surface, by a layer height, sometimes constrained by the topology of the model. Is the picture you included stuff that you've printed, or something that you're trying to print?