The Federal Trade Commission has published guidelines for advertising mobile applications. In general, the guidelines incorporate the FTC’s policies on truthful advertising and data privacy. On the advertising side, if you make objective claims about your app, then you will need proof to support your claims. The proof necessary to support objective clams is competent and reliable evidence. And if your claims provide for certain benefits such as health and safety benefits, then you will need competent and reliable scientific evidence. This generally requires the opinion of experts in the relevant field of the benefit your app claims to offer.
If a disclosure is necessary to make your objective claims accurate, then the disclosure needs to be clear and conspicuous. There is no specific rule on font size or type, but the disclosure should be in a font size and location where consumers will notice it. Don’t bury a disclosure in dense blocks of text or in hyperlinks.