I am so sorry but your betta is very sick. He is probably very sick because he is being slowly poisoned with his own waste products. If he is in this size tank and is not heated and filtered the tank cannot cycle and he cannot get rid of the
ammonia in the water any way but through water changes. One time a week is not enough in this instance. It would need to be done daily to really help. And even with the water changes I am not sure it will help at this point because the betta is probably also cold. If his temperature is not warm enough or kept at a steady temperature all the time, he will probably not make it because his metabolism slows every time he cools down and speeds up when the water gets warmer. This makes his whole system react negatively. He cannot digest his food well and will become constipated and eventually die.
He really needs to be in a tank where it is capable of heating (at least 3 gallons) and then the tank needs to cycle and until it does he needs to have a filter running but also daily water changes of at least one third of his water. You need to be testing the ammonia levels of his water every day to make sure he is safe and not being poisoned.
He will probably not eat flakes for you too much as most bettas will not eat them easily. They usually do prefer pellets but you must watch how many you give them as they will make the betta constipated if you feed them too many.
Bettafix is also not a good medicine for bettas. It contains tea tree oil and that is not good for their Labyrinth organ. I would do a
water change and not put any more of the Bettafix back in the tank.
I am so sorry that he is sick but he really does need to be in a bigger container with a heater and filter. Is there any way you can do this for him?
Rose