I have abeen asked to restore a painting, how to tell if a painting is oil or acrylic?

I have been asked to restore a painting that is on a big flag/banner ith knig william on it, it is very worn and has big cracks all over it where the paint has come off. I need to fill in the cracks to bring the painting back to its original look. It feels like it has a varnish coat over the top of the paint but I dont even know if the painting is oil or acrylic,how would I know for sure before applying the wong paint, I think it might be acrylic with varnish over the top so will I be able to paint over the varnish? And should I varnish again once I am finished restoring it?