A software program and the icons it uses are generally not considered derived works of each other under copyright law. This means that there is no interaction between the license used for the icons and the license used for the software. The licenses do not even have to be compatible with each other.
That said, the CC-BY license of the icons does place some requirements on you, and the proposed
CREDITS.txt file might not fulfill them.
One of the requirements is that the attribution given to the author of the icons must be in the same place and equally prominent as other attributions you give. Those other attributions would also include third-party libraries.
If you already have a
Help->About box and/or a
README.txt file where you mention the third-party libraries you use, then you must put the attribution for the icons there as well.
If you don't have any source/library credits yet, then collecting all credits in a
CREDITS.txt file is ok, provided that the file is distributed with all copies of your program (also the binary-only distributions).
tl;dr: Every distribution of your program with the icons must contain an attribution to the icon's author in some way. This can be a
Help->About screen or a separate file. If you also attribute authors of other works (such as libraries), all attributions must be collected together.