SkinGPT-4, a large vision-language model, leverages annotated skin disease images to augment clinical workflows in underserved communities. However, its training dataset predominantly represents lighter skin tones, limiting diagnostic accuracy for darker tones. Here, we evaluated performance biases in SkinGPT-4 across skin tones on common skin diseases, including eczema, allergic-contact dermatitis, and psoriasis using the open-sourced SCIN dataset. We leveraged the SkinGPT-4 backbone to develop finetuned models for custom skin disease classification tasks and explored bias mitigation strategies. Clinical evaluation by board-certified dermatologists on six relevant skin diseases from 300 SCIN cases assessed images for diagnostic accuracy, informativity, physician utility, and patient utility. Model fairness metrics, including demographic parity and equalized odds, were calculated across skin tones. SkinGPT-4 achieved an average demographic parity of 0.10 across Fitzpatrick types, with notable differences of 0.10-0.15 between lightest and darkest tones across evaluation metrics. Model hallucinations in artifacts and anatomy occurred at a rate of 17.8. Our customized models achieved average F1, precision, and AUROC of 0.75, 0.78, and 0.78 across visually similar disease pairs. Fairness analysis showed an average demographic parity of 0.75, with a maximum disparity of 0.21 across skin tones. The best model achieved parity scores of 0.83, 0.83, 0.76, 0.89, 0.90, and 0.90 for Fitzpatrick I-VI, indicating robust fairness. Large language models such as SkinGPT-4 showed weaker performance on darker tones. Model biases exist across evaluation criteria, and hallucinations may affect diagnostic efficacy. These findings demonstrate the efficacy of training accurate, fair models using existing backbones for custom skin disease classification.