I have done some digging you definitely got the decade right. If you can see the WPL search it appears with the exact company name but why it says it's wool is beyond my understanding. So after I hit rocks with research I contacted NY librarians with the query and I got the following response
Business Reference Librarian
Sep 12 2022, 11:38am via System
Denitsa Kovacheva
We have a guide on researching old companies at
https://guides.loc.gov/historical-company-research
I did try and find out information but I came to a brick wall.
As for the one you mention I did find the Trademark for A. Flaster from 1953. Our holdings for things can be spotty but I am attaching somethin from late 50s telephone book and you will notice that it A. Flaster Originals is listed as is Irving Flaster, Irving Flaster Inc. and Flaster & Co. which are all related by name or address. I tried to find out more using ancestry.com but didn't find much. I think I did find him; a WWII draft card for an Irving Flaster was living in the Bronx (wife Bess) was born in 1911 and worked at Domestic Broadtail Producers Inc (broadtail is related to coat making). the 1940 and 1950 Censuses have him working at a furrier though no name was given. He is listed in 1949 but the business were not (see attached). However, Irving was listed in 1946 and there was a Flaster Inc (furs) and Flaster & Warm ie Murry J Flaster) which I definitely suspect is related though this couldn't tell how (Murry not listed in 1949).
I did look in our Apparel trades book but we don't have holdings between 1948-1958 on-site. I looked in Brooklyn and the Manhattan/Bronx section and there didn't seem to be anything listed in 1947 or 1959. I did look under Hewlett but which there was a Hewlett in Nassau County (nothin by those business names listed) there was no Hewlett Park.
I know there was an Alfred A. Flaster operating in New York in the 30s and 40s that did glass perfume bottles and I mention it because it may be related in some fashion that may be determined with more information, though it doesn't seem overtly related at the moment. I think most were sold via the Theon Company started by a Marcella Flaster (Alfred's wife in the 1940 Census) and from what I have seen it may have been on 5th Avenue but Alfred's WWII draft card put the business at that time at 25 W 18th. I don't know of these people are related but Flaster is not a common name.
I hope this is helpful but please let us know if we can provide any further assistance.
Business Reference Services / ebt
Library of Congress
http://www.loc.gov/rr/business/
https://blogs.loc.gov/inside_adams/
As you see a lot of the information hit dead end, I only found that A Flaster originals had couple of patents circa 1954, so my wild guess is your coat is dated to back then.
