The fluorochromes usually do not interfere with the antigen binding. If they did, the antibody would not be much use. The issue of using antibodies across methods is really what is the condition and accessibility of the antigen. In Flow cytometry the target antigen is almost always in the native state. In Western Blots it is almost always denatured. The epitopes for antigen binding may be destroyed in the denatured state. Without any data the best way is just to test your antibody in the method of choice and see if it works.

James Drummond thanks for your answer! I didn’t consider that issue but I’ll see if it works... With the question I meant that there could be interference between the FC Ab (used as primary) and secondary Ab, because of the flurorochrome bound to the Fc of the former.

Try doing a dot blot with your primary, let it dry, and then come in with the secondary as if it was a western blot and see if it works.