Is spraying soapy water fine during flowering (1 week into flower on an autoflower)?

You will be smoking anything you spray onto the flowers. Spraying will also increase the chances of bud rot. There should be no need to spray unless there are actually insects infesting your plant. Once flowering and trichome production begins, insects should not be a real problem, you may get the odd one, but it is far better to remove them by hand than spray your entire plant. Cannabis is almost bullet proof when it comes to insects, unless your plants are weak and/or diseased. Hope this helps,.......... Organoman.