I would be less worried about clothing and more worried about my skin and eyes - black light is mostly ultraviolet, which is invisible (but can be very destructive).

Why black light for plants?? Photosynthesis, plant development and flowering is mostly controlled by red and blue light. It is true that the average incandescent is too yellow for optimal plant growth while the average fluorescent is too green. But it is possible to get fluorescent tubes that are close to the color of sunlight with little UV. That seems a far better choice for growing plants.

Just ask the store for 'full spectrum' fluorescents. T5 is a good type.