Can a medical discharge/chapter be stopped once it has been started during basic training?

The bar for initial entry separations is very low. You are probably unfamiliar with Army regulations and your son definitely is. He is not receiving a medical separation from a Medical Evaluation Board as AR 40-501 would dictate because he's still an Initial Entry Soldier. He will probably receive an uncharacterized Entry Level Separation.

The recommendation will be made by a PA or NP and reviewed by either a senior PA, NP or Doctor. Offering your unsolicited medical advice on a case you are removed from will not be helpful.

You can call a Congressionman if you like. They will contact the medical section and the provider will show that the Soldier is not medically fit to serve. The Soldier does not have to be diagnosed with anything to prove that they are simply not medically fit enough for service.

No doubt he is feeling defeated, but he's an adult and has to work through this on his own, and that will make him stronger in the future. Not everyone is meant to be a Soldier

First off, you have absolutely zero reasoning as a family member to be emailing or calling anyone in his chain of command. You are a family member and absolutely zero individuals within the armed forces has to engage with you. Also, although you are correct with referring to 40-503, they have likely spoken to MEDCOM and MEPCOM and are using DODI 6130.03 which states under disqualifying conditions:
Any abnormal findings on imaging or other examination of body structure, such as the lungs, diaphragm, or other thoracic or abdominal organs, unless the findings have been evaluated and further surveillance or treatment is not required.
b. Current abscess of the lung or mediastinum.
c. Infectious pneumonia within the last 3 months.
d. History of recurrent (2 or more episodes within an 18 month period) infectious pneumonia after the 13th birthday.
e. History of airway hyper responsiveness including asthma, reactive airway disease, exercise-induced bronchospasm or asthmatic bronchitis, after the 13th birthday.
Symptoms suggestive of airway hyper responsiveness include but are not limited to cough, wheeze, chest tightness, dyspnea or functional exercise limitations after the 13th birthday.
(2) History of prescription or use of medication (including but not limited to inhaled or oral corticosteroids, leukotriene receptor antagonists, or any beta agonists) for airway hyper responsiveness after the 13th birthday.
f. Chronic obstructive pulmonary disease including but not limited to bullous or generalized pulmonary emphysema or chronic bronchitis.
g. Bronchiectasis (after the 1st birthday).
h. Bronchopleural fistula, unless resolved with no sequelae.
i. Current chest wall malformation, including but not limited to pectus excavatum or pectus carinatum which has been symptomatic, interfered with vigorous physical exertion, has been recommended for surgery, or may interfere with wearing military equipment.
j. History of empyema unless resolved with no sequelae.
k. Interstitial lung disease including pulmonary fibrosis.
l. Current foreign body in lung, trachea, or bronchus.
m. History of thoracic surgery including open and endoscopic procedures. n. Pleurisy or pleural effusion within the previous 3 months.
o. History of spontaneous pneumothorax occurring within the past 2 years, or pneumothorax due to trauma or surgery occurring within the past year.
p. Recurrent spontaneous pneumothorax.
q. History of chest wall surgery, including breast, during the preceding 6 months, or with persistent functional limitations.

From reading your post and reading 6130.03, your son has a disqualifying condition which should have prevented him from enlistment.

Legal isn’t going to help you, emailing his command isn’t going to help you. The discharge began at the doctors, got a legal review stating the discharge is justified, and the command has approved it. The discharge will continue and there isn’t anything you can honestly do about it.

If this is his second time at basic, he has clearly not met all requirements. If there is “black mold” in his camel back, that is because he failed to clean his equipment. Who analyzed his camelback for mold? You? The Army? From the “surface” it looks like your son cannot conform to the military way of life. Take the medical and be glad that it’s not something else.