Your fish looks.. very stressed and unwell.
1/2 gallon tank isn't very big. Then take out the water displaced by rocks and decoration - he's living in just a few cupfuls of water. If you're changing that water once a week, it'll be loaded with ammonia most of the time, which will not be helping his health at all.
He should be eating twice a day, small amounts, as you're using flakes (these also cause a lot of ammonia..). Flakes aren't great, I noticed my first betta got very bloaty on them at times - he took time to want to eat pellets but did so after I stopped giving him flakes and let him go hungry a few days if he didn't eat them. Irregular/infrequent feeding seems to be almost as bad for them as overfeeding (though stupid pet store people tell folks to feed thier bettas every few days.. they are much better off with daily small meals..)
I've never had a fish with swim bladder issues, so I'll leave that side of it to someone who's dealt with it. But please do consider a bigger living space, without sharp plastic plants and with much more frequent water changes (or at least 2-3 a week in his present home!). Some bettas freak out badly in bowls, the round shape distorts everything.. if you do choose to allow him a larger home, perhaps a try a rectangular one, it might help him not to stress.
What's your routine for water changes now? Where do you put him for them and do you acclimate him to the new water at all?