[voci]

Compilado con delphi 10.3.3 y probado en mi móvil con android 7.

Código Delphi [-]
unit Unit1;

interface

uses
  System.SysUtils, System.Types, System.UITypes, System.Classes, System.Variants,
  FMX.Types, FMX.Controls, FMX.Forms, FMX.Graphics, FMX.Dialogs, System.Permissions,
  Androidapi.Helpers, Androidapi.JNI.Os, Androidapi.JNI.JavaTypes;
type
  TFConfigIP = class(TForm)
    procedure FormShow(Sender: TObject);
  private
    { Private declarations }
    procedure PermisoEscrituraLectura;
    procedure Servidor;
  public
    { Public declarations }
  end;

var
  FConfigIP: TFConfigIP;

implementation

{$R *.fmx}

procedure TFConfigIP.FormShow(Sender: TObject);
begin
  if (PermissionsService.IsPermissionGranted(JStringToString(TJManifest_permission.JavaClass.READ_EXTERNA  L_STORAGE))= false) or (PermissionsService.IsPermissionGranted(JStringToString(TJManifest_permission.JavaClass.WRITE_EXTERN  AL_STORAGE))= false) then
    PermisoEscrituraLectura
  else
    Servidor;
end;


procedure TFConfigIP.PermisoEscrituraLectura;
begin
  PermissionsService.RequestPermissions([JStringToString(TJManifest_permission.JavaClass.READ_EXTERNAL_STORAGE), JStringToString(TJManifest_permission.JavaClass.WRITE_EXTERNAL_STORAGE)],
  procedure(const APermissions: TArray<string>; const AGrantResults: TArray)
  begin
    if (Length(AGrantResults) = 2) and (AGrantResults[0] = TPermissionStatus.Granted) and (AGrantResults[1] = TPermissionStatus.Granted) then
      begin
        ShowMessage( 'Permiso concedido.');
        Servidor;
      end
    else
      ShowMessage( 'Permiso denegado.');
  end)
end;

procedure TFConfigIP.Servidor;
begin

end;

end.

Saludos.