you may fall foul of this:
3.1.2. New entrants to the Armed Forces undergo intensive training that is both physically arduous and mentally taxing. They must be of robust
constitution and free from disease or injury that prevents them from meeting the challenge. During service they may operate in locations remote from medical care. It follows that those predisposed to, or with, conditions requiring periodic medical care or review, taking long term medication, or in whom deterioration of a pre-existing condition might occur are not suitable for military service. Additionally, modern Armed Forces operate with minimal manning margins so that illness, especially in key personnel, may have an immediate and even profound impact upon operational effectiveness.
Furthermore, flexibility of employment, in the event of illness, is limited. These constraints place considerable reliance upon screening at the entry medical examination, to ensure that those recruits that are accepted start their training with the best chance of success and subsequently serve, for the period of their engagement as fit, healthy and dependable service men and women.
You won't know until you try though. Have you actually been diagnosed with reflux? are you self medicating or being prescribed anything? Have you been tested for H-pylori?