You will need an adapter placed between the VGA-Mac adapter and the computer that adds a horizontal and vertical sync signal.
The most common mistake when using an inline adapter with a VGA-based display such as the Basic Color Monitor on a G3 is to set the adapter to VGA/SVGA. If you already have an inline adapter that converts the pinouts from VGA to DB15 (which in the case of the Basic Color Monitor you would), then the second inline adapter would only need to be set to provide the two separate sync signals. The rest of the adapter should be set to an open state. Most VGA to DB15 adapters do not provide the additional horizontal and vertical sync signals and that is why the second adapter is needed.
In some instances you will also need to initially reset the PRAM on the Macintosh G3 after the adapters have been set correctly to establish the proper sync signal.