it will be difficult to accept private collector's submission for testing.
(1)
before the Fleuritest, COSC and Chronofiable tests must be done and the
certification must be shown. Next is the aesthetic aspects, the watch
must be stripped down to component-level for visual examination.
(2)
cost involved .... the brand supposedly to pay an annual fee of
CHF10,000 per year regardless of quantity to be tested. The individual
charge per piece is not significant at CHF 45.
(3) A single
piece or a few pieces of one brand and a specific model is not a good
representation. Will be unfair for the brand/s which the private
collector/s send in to test and the unfavorable results will cause
potential issues.
From the above, it is very unlikely FQF will accept non-brand for the Fleuritest.
You could try to simulate after matching your watch with the atomic clock (online) by following the activities 
Kong