Checked through quite a few sources and the most info comes from British sources that say the Whitechapel gunmaker, Ezekiel Baker got the invitation to the competition due to relationship with the Prince Regent, whatever that's worth. His original submission were musket sized and musket bored (.775) and were dropped like a hot rock. He was given a German jaeger rifle and told to make something like this Zeke! The accepted gun was shorter and of 'carbine-bore' of .625" and a 30 inch barrel with 7 grooves, with a twist of 1 turn in 10 feet (which was 1/4 turn in the barrel's length). Once accepted, 800 rifles were ordered in March, 1800, through various gunmakers in London and Birmingham for issue to the 95th, later the Rifle Regiment. Before the Napoleonic Wars were over, the Baker rifle was in use by the 95th, some skirmishers of the Light Regiments, the 60th (Royal Americans), and the light companies of the King's German Legion. In addition, Portuguese rifle companies of the Cazadores which were basically their Light troops. 20 years later the rifles showed up in the hands of Santa Anna's light troops (Cazadors, chasseurs, riflemen...take your pick) and after San Jacinto the records show that among the captured weapons were "jaegers with sabers", the description of baker Rifles and their sword bayonets...and we're back to jaegers!
I'd have to say that a .69 Baker was either a special modern project or an incorrect bore measurement.