You will not be able to see the Milky Way and stars when it is raining. Also, the Milky Way can only be seen if you go to to the darkest parts of Singapore like Lim Chu Kang, Changi area and when it is very clear (no clouds and no moon), then there is a small chance that you can see a hint of it. In short, it is difficult to see and even more difficult if you do not know how it looks like.
The Milky Way is a very long stretch. It stretches from horizon to horizon and at a dark place it looks like a grey colour cloud with structure. At a very very dark place, it glows brightly and has much details. The 'cloud' is actually many many stars that our eyes cannot resolve.