Details of Brown's observations, concerning both the pollen and the microscope, are given by Pearle et al. in What Brown saw and you can too. The pollen was from the flower Clarkia pulchella, a.k.a. pinkfairy, ragged robin, or deerhorn clarkia, discovered on the return trip of the Lewis and Clark expedition by Lewis on June 1, 1806. He wrote in his journal: "I met with a singular plant today in blume, of which I preserved a specemine. It grows on the steep sides of the fertile hills near this place...". To England seeds of Clarkia were brought only in 1826 by the expedition to the American northwest led by David Douglas, that begun on July 25, 1824 and was sponsored by the Horticultural Society of London and the Hudson's Bay Company. The society grew the flowers in its garden in Chiswick.
In Brown's Slips Catalogue, dated June 12, 1827 and June 13, 1827 some sheets are labeled Clarkia with a line in Brown's handwriting having "Hort Soc (Horticultural Soc) Horticult (illegible) Chiswick (illegible)". The next line reads "occident (western) Amer (illegible) by D Douglas". The results of his observations were reported in the paper R. Brown, A brief account of microscopical observations made in the months of June, July, and August, 1827, on the Particles contained in the Pollen of Plants; and
on the general existence of active molecules in organic and inorganic bodies, Edinburgh New Philos. J. 5 358-371 (1828); reprinted in Philos. Mag. 4 161-173 (1828). The first paragraph described the microscope:
"The observations, of which it is my object to give a summary in the following pages, have all been made with a simple microscope, and indeed with one and the same lens, the focal length of which is about 1/32 of an inch".
By the 10 inch rule of thumb (the near object is best seen from 10 inches away, so the magnification is roughly 10/focal length) the magnification of Brown's microscope was then about $\times 320$, Brown's own estimate was $\times 370$. The two preserved Brown's microscopes, one at Kew Gardens and the other at the Linnean Society, have $\times 170$ lenses, so it probably was not one of them. The basic design goes back to Leeuwenhoek (1674), who already achieved magnification of $\times 300$ and observed bacteria through his microscope, see History of Microscopes timeline.