This is not at all straightforward to answer. The problem is that prior to the 1976 US Copyright Act, all works had to be registered to gain protection. Registration was initially for 28 years, and provided this was properly renewed in the 27th year, it could be extended to 56 years. Any work which was still in copyright when the 1976 Act came into force, would have benefited from having 95 years added onto its original period of protection. Much more detailed information about this can be found in this pdf
The fact that TWA as a company ceased to exist in 2001 does not alter this situation as all the assets (including the intellectual property) of TWA were taken over by American Airlines
I think we have to assume that TWA or David Klein would have registered these paintings in the prescribed manner and therefore since he appears to have started producing these posters in 1955, they would have been in copyright at the time the 1976 Act came into force (1955 + 28 = 1983). The best clue, if you have access to one of the posters, is to look for the copyright notice (something like: © David Klein 1955 or © TWA 1955). If there is no such notice and it's a genuine, complete, poster then chances are it was not correctly registered. However what is less clear is who might own the copyright today. If David Klein retained copyright then you would need to contact his estate (see bottom of this page
. However if when he was commissioned by TWA he transferred the copyright to TWA, then American Airlines will most likely own the copyright today. I suggest you contact Klein's estate about this.
However, if my assumption is wrong about the works having been registered (it's amazing how many artists and writers did not do this correctly), then the works will be in the public domain. You can find out about registrations by contacting the US Copyright Office
. Unfortunately their online catalogs do not contain details of pre-1976 artistic works, so you would probably need to ask for a manual search to be done, for which a fee is payable.