I am afraid such capability is not supported yet in QuickApps, especially qListForm. Typically you would construct the Form Component Behavior on the field you are interested in. The problem is that the condition or criteria for field behavior currently does not support built-in properties such as [Me], [CurrentLoginUser] and etc. and there is no condition based on current user in certain SharePoint group (as in ShowUserGroup/HideUserGroup). Typically a List Item has CreatedBy, ModifiedBy user/group field and those field can be involved in current FCB condition. If your scenario supports the use of these fields, then you are in luck, otherwise, as an one off solution, you could build JavaScript solution to disable the button based on the condition for checking current user.