Well, most of those colors are relatively generic and can be purchased by any manufacturer (ie Testors, ModelMasters, Tamiya, etc; I'm not even sure Academy sells paint). As for the number, historically, the Federal Standard 595B specification is a U.S. government paint color specification system that assigns numbers to colors in a loose arrangement which is used to designate a paint color.
The first digit signifies opacity (correct word?):
1 - Gloss
2 - Flat
3 - Clear (?) (i.e. clear red)
Generally the second digit of a color signifies general color:
0 - Brown
1 - Red
2 - Orange
3 - Yellow
4 - Green
5 - Blue
6 - Gray
7 - Other (white, black, violet, metallic)
8 - Fluorescent
For others out there please correct me if I'm wrong, but in the last three digits, the numbers 100-999 represent the sahdes of the color from dark to light respectively. For say, Olive Drab, A number like 24xxx and 24yyy (x and y representing two different shades) may still be clasified as Olive Drab but as different shades.
So in your colors you listed, FS numbers F.S. 25187, F.S. 25526, F.S. 25450, for example, and say we didn't know what colors they were, by looking at our reference we can tell all three are a flat (first number is 2), Blue (second is a 5), and the three different last 3 digit numbers show various shades. If you go to any modeling store or a store of any kind that sells model paint, some manufacturers give the FS number with it. If by chance, say we go in a store, find paints with those exact numbers, we would find out that the colors are Dark Blue, Blue Gray, and Light Blue, respectively.
The FS numbers on the instructions and what is available won't always match up number for number. Generally when that happens I settle for a paint close to the number (i.e. there is no 25526, so I settle for 25527; keep it as close as you can). When this happens you can look at both FS numbers and add black or white to darken or lighten the color depending on the required paint and the available paint.
This kinda came off more complicated than I expected, so if there is any (*cough* or all) that you don't understand, please don't hesitate to ask me or anyone else for a clearer response. I promise I'll try to be clearer.