I would like to know if there is some online source where Boardman's 1964 thesis is available or his Warwick mimeographed notes. This is because by what I've heard Boardman's construction has a more modern or categorical feel to it than Adams's account in his blue book and I would love to look at Boardman's construction with modern eyes, taking into account all we've learned about the $\infty$-category of spectra in the last years.
Boardman's thesis was (re)published a year later as three separate booklets, and a PDF scan of all three booklets is available on my scans page:
J. M. Boardman. Stable homotopy theory.
University of Warwick, Coventry.
Chapters I–IV: 42 pages, November 1965.
Chapter V: Duality and Thom spectra, 66 pages, January 1966.
Chapter VI: Unoriented bordism and cobordism, 71 pages, July 1966.
Here is a link to Duality and Thom Spectra, which is the fifth part of the notes by J. M. Boardman that were mimeographed at the University of Warwick in 1965–1966 and covered the material in his 1964 Ph.D. thesis from Cambridge University, On Stable Homotopy Theory and Some Applications.
Reinhard Schulz, who has posted this file on his web site explains that parts 1-4 of Boardman’s notes are discussed in the proceedings of the 1998 conference held in honor of Professor Boardman’s sixtieth birthday.
Boardman's Ph.D. thesis is available at the Cambridge University Library: https://idiscover.lib.cam.ac.uk/primo-explore/fulldisplay?docid=44CAM_ALMA21579046710003606&vid=44CAM_PROD
The library refuses to lend it out through an interlibrary loan, so it appears that the way to go is for somebody at Cambridge to physically visit the library and scan the thesis.