Вам нужно будет использовать WinINet в Вашей TfrmMain:

Uses WinINet;

и добавить к TButton следующий обработчик btnEmptyCache:

Procedure TfrmMain.btnEmptyCacheClick( Sender : TObject );
Var
    lpEntryInfo : PInternetCacheEntryInfo;
    hCacheDir   : LongWord;
    dwEntrySize : LongWord;
    dwLastError : LongWord;
Begin
    dwEntrySize := 0;
    FindFirstUrlCacheEntry( NIL, TInternetCacheEntryInfo( NIL^ ), dwEntrySize );
    GetMem( lpEntryInfo, dwEntrySize );
    hCacheDir := FindFirstUrlCacheEntry( NIL, lpEntryInfo^, dwEntrySize );
    If ( hCacheDir <> 0 ) Then
        DeleteUrlCacheEntry( lpEntryInfo^.lpszSourceUrlName );
    FreeMem( lpEntryInfo );
    Repeat
        dwEntrySize := 0;
        FindNextUrlCacheEntry( hCacheDir, TInternetCacheEntryInfo( NIL^ ), dwEntrySize );
        dwLastError := GetLastError();
        If ( GetLastError = ERROR_INSUFFICIENT_BUFFER ) Then Begin
            GetMem( lpEntryInfo, dwEntrySize );
            If ( FindNextUrlCacheEntry( hCacheDir, lpEntryInfo^, dwEntrySize ) ) Then
                DeleteUrlCacheEntry( lpEntryInfo^.lpszSourceUrlName );
            FreeMem(lpEntryInfo);
        End;
    Until ( dwLastError = ERROR_NO_MORE_ITEMS );
End;