TL;DR: Yes, you can drink black tea on an empty stomach; however, it may cause acidity although this greatly depends on the type and quality of the tea.
Typically, it is better to consume tea after meals and snacks as this will help in digestion and activate your metabolism to break down the food.
Tea is generally good for your health consuming black tea can result in healthier living provided it replaces other sugary drinks in your diet. This will result in a reduction in the amount of sugar and calories in your daily intake which will result in a healthier body-mass index in the long term (depending on your age, build, health condition, etc.).
Green tea has been shown to activate your metabolism and increase your metabolic rate which results in faster burning of fat/calories per day. See this article for more: Green Tea Boosts Metabolism, Protects Against Diseases [WebMD].
Black tea while also being very good for you has not been shown to have the same efficacy with regard to health as green tea and thus, I would recommend a cross between a green tea and black tea for the purpose of “health”.
If you want a high quality regular green tea try this wonderful Darjeeling green: The Jade of Bengal | Single-Estate Darjeeling Green Tea
Note: This recommendation is for green tea/black tea which is unsweetened and without the addition of any other materials. We highly recommend using only high quality loose leaf tea to brew the tea in order to get the nutritional/mineral benefits.
[This is a guest post from noted tea expert, Peter Strantham]