In researching this question and discussing with @conifold I came to two conclusions. Firstly, that Priestly was active and interactive in the scientific community almost to the month of his death. Secondly, that there is far less support for the suggestion that it is believed that he was rejected from the scientific community due to the Phlogiston debate than was my original impression based on some popular accounts. There is a great deal of believe that Priestley was wrong, but that is not the question I asked.
Having said that, I do believe that a question should be answered in the spirit in which it was asked (this time by me). So with acknowledgement to @conifold for helpful comments (see the chat) I give the result of my research on the matter.
It has been stated in several popular sources that in his later career, Joseph
Priestly became isolated from the orthodox scientific community due to his
continued and unpopular support for the Phlogiston theory then eschewed by the
community at large.
"However, Priestley's determination to defend phlogiston theory and to reject
what would become the chemical revolution eventually left him isolated within
the scientific community".
This seems to be a misrepresentation of the situation.
Priestly did not start the theory of phlogiston, he used it.
Stahl is usually credited with developing the theory in 1703,
but the word had been used in 1606 in more or less the same way.
Priestly was born 1733, so by the time he was say, 30, it was
like being a follower of Einstein in the 1960s. Stahl was generally
recognised as giving a good rational theory of some chemical reactions.
Priestly was not a recluse. He had engaged in the late 1700s in a variety
of pamphlet campaigns, some of which were considered rather inflamatory
and he spoke out against the reformed church. He was described by his
opponents as a conflict between a priestly politician and a political
Lavoisier wrote on oxygen (which he mistakenly named acid maker) in 1775
with his Easter Paper to the French Academy. And then started the anti
phlogiston movement by responding to Priestly's complaints that Lavoisier
had not acknoweldged Priestly's work in the matter, by claiming that Priestly
totally misunderstood the experiments and deserved no credit.
Cavendish in England is said to be
the first person to start working with the oxygen theory around 1787,
however, his papers on this at this time show a mild favoring of the
Phlogiston theory. He also developed a theory that effectively
equated Phlogiston with Hydrogen, and did a better job of explaining
acid reactions than did Lavoisier.
However, by 1797, Kant reported that the Phlogiston theory had been
replaced by the Oxygen theory in a rapid change of opinion within the
scientific establishment. In 1797, Priestly wrote Observations on
Phlogiston and the decomposition of water - which was effectively an
explicit defence of the Phlogiston theory against the Oxygen theory.
In 1800, Priestly, himself, was explicitly identifying Phlogiston with
Hydrogen rather than oxygen. This is was not a turn around, as the
identification of Phlogiston with negative oxygen, a common notion
today, was not inevitable. The core issue was to explain the chemical
reactions by combinatorics of elements. The details had been under
flux for a couple of centuries and would continue to be so for another
In November of 1801, Priestly responded to a paper by Cruickshank
regarding the chemistry of carbon monoxide. Priestly supported the
Phlogiston theory. However, for 1802 and 1803 he seems to have focused
on other scientific work. In Priestly's career, the Phlogiston theory
was not everything, he defended it strongly and rationally, and does not
seem to ever have been converted to the Lavoisier school. But, he defended
it in interaction with, and even with some support from, the scientific
community of the time.
Priestly died in early 1804. It is hard to say what would have happened
next. He might have become a crank ranting about a discarded theory, or
he might have been converted, or he might have continued to be no longer
interested enough to continue the debate. But, he died, and there seems
to be no period of his life in which the image of Priestly rejected by
the orthodox science for his loudly proclaimed views is justified.