As Alam said, choosing CVI indicators is subjective and based on the study scope, whether the focus on socioeconomic factors or physical factors. However, some indicators, in my opinion, are very essential, such as the coastal slope, elevation and land use-land cover.
Anyway, CVI studies usually involved about four to eight factors, and weighting or evaluating these factors is done using spatial tools available in GIS.
I hope you find my article useful in this matter:
Article Vulnerability of Kuwait coast to sea level rise