"There was a series of math books, which started Arithmetic for the Practical Man, and then Algebra for the Practical Man, and then Trigonometry for the Practical Man, and I learned trigonometry for the practical man from that. I soon forgot it again because I didn't understand it very well but the series was coming out, and the library was going to get Calculus for the Practical Man and I knew by this time by reading the Encyclopedia that calculus was an important subject...and then the calculus book finally came out ...and I went to the library to take it out and she looks at me and she says, "Oh, you're just a child, what are you taking this book out for, this book is a [book for adults]." So this was one of the few times in my life I was uncomfortable and I lied and I said it was for my father, he selected it. So I took it home and I learnt calculus from it..."
Calculus for the Practical Man was first published in 1931 when Feynman was about 13 years old, which fits the story (he was waiting for the book's publication).
So that would point to Feynman's calculus book being "Calculus for the Practical Man" by J.E.Thompson rather than Silvanus P Thompson's "Calculus Made Easy", whose second edition came out in 1914. I would not be surprised that Feynman read and used both.
The two books are quite different in approach, Practical having, to me, a rather unique physics orientation and being a more demanding text.