Aside from the Angels "Flashback Friday" caps that were released recently, multiple caps for this season's "Turn Back The Clock" games have been released in the modern 100% polyester "Cool Base" style. Availability varies, and they can be found at hatlclub.com, ecapcity.com, and the mlb.com shop. Here are the caps that have been released to the general public thus far:
Tampa Bay Rays as the 1940s "Tampa Bay Smokers"
1940s St. Louis Cardinals
Los Angeles Dodgers as the 1940s "Brooklyn Dodgers"
Early 1980s Seattle Mariners
Washington Nationals as 1930s "Washington Senators"
1970s Atlanta Braves, made for the "Civil Rights Game"
1930s San Diego Padres "Pacific Coast League"
1970s/80s Philadelphia Phillies
Early 1970s Pittsburgh Pirates
Kansas City Royals (I can't find any further information, any help is appreciated)
1960s Baltimore Orioles
More caps are expected to be released throughout the season, I will post any more caps that are released here on the Ballcap Blog. Certain Turn Back The Clock caps haven't been released to retail (yet), such as the 1918 caps that the Cubs and Red Sox wore, and the 80s Padres "Taco Bell" cap.