A quick search online for Isaac Barnes' registered designs at TNA has revealed the following entries, not all of which are Class 3 (glass):
Class 3: RD 149521 of 22 February 1862 – glass globe or shade.
Class 3: RD 149522 of 22 February 1862 – glass globe or shade.
Class 1 (metal): RD 157197 of 3 November 1862 – cap or cover for globes or glasses of gas and other lamps.
Class 3: Rd 163192 of 9 June 1863 – gas chandelier.
Class 3: RD 163900 of 1 July 1863 – chandelier.
Class 4 (earthenware): RD 189872 of 21 September 1865 – smoke cap or cover for the globes or shades of lamps.
Class 4 (earthenware): RD 189873 of 21 September 1865 – smoke cap or cover for the globes or shades of lamps.
Class 3: RD 256680 of 13 October 1871 – chandelier.
Class 3: RD 271867 of 5 April 1873 – chandelier.
Class 3: RD 281119 of 13 March 1874 – design for turning on gas lamp for lighting.
Class 1 (metal): RD 283836 of 20 July 1874 – chandelier.
Class 3: RD 305227 of 17 November 1876 – no subject.
Class 3: RD 324501 of 2 August 1878 – no subject.
Class 3: RD 329744 of 28 December 1878 (though Raymond Slack gives the date as 28 November 1878, and his interpretation seems to be confirmed by the somewhat illegible entry copy in Jenny Thompson, page 119) – no subject.
Sadly, there seems to be no direct mention of the flower troughs – perhaps they are the entries without a subject.
The designs themselves are typical of many Victorian glass registrations – an abundance of chandeliers, globes, shades, and other glass bits and bobs connected with lighting. It just makes one realise that lighting the home or other premises before the advent of electric light was a struggle to maximise the output of any light source, and that maintaining and cleaning the paraphernalia associated with it often took up significant amounts of time and effort (especially with oil- and candle-lighting).
Googling Isaac Barnes and Birmingham in all kinds of combinations with other keywords has proved to be unfruitful so far.
Broad Street was (and still is) in the commercial heart of Birmingham, and the Barnes addresses there are more likely indicative of retail or office premises rather than a glass manufacturing site. The Cambridge Street address is only a short distance from the extensive Birmingham canal network (as are most other central Birmingham addresses), but the site is presently in a development area, and any Victorian retail or manufacturing premises seem to have disappeared, though the site seems unlikely to have housed a glassworks of any scale. I think the most likely scenario is that Barnes was a retailer or agent for chandeliers, lighting appliances and accessories (perhaps also dealing with other fancy goods), and that the manufacture of the wares from his registered designs would almost certainly have been contracted out to one of the myriad manufacturing businesses operating throughout the area.
Fred.