You always have cross-reaction between species. As your antibodies are in excess compared to the immunoprecipitated proteins, you are forcing the recognition of the antibodies by your secondary antibodies no matter the species it is. An alternative to your anti-rabbit would be to use a protein G conjugated with your dye (peroxydase or fluorescent). Protein G only recognize native IgG and therefore would recognize your primary antibody but not the IgG you used to immunoprecipitate your protein of interest.This is not 100 % efficient but at least you lower the signal of the IP-IgG.
Sounds like your Goat Anti-Rabbit secondary is cross-reacting with Mouse IgH+L? Do you know if the GaRabIg preparation was "absorbed" against Mouse Ig to remove cross-reactive specificities?
it seems that your secondary goat anti-rabbit is cross-reactive to your mouse antibody. Try a different anti-rabbit antibody that is specified not to cross-react to mouse antibodies.
Have you tried your Western omitting the primary antibody (raised in rabbit) and see if you still get the signal? This is just to confirm that what you detect is actually the light/heavy chain and not a cross reacting protein?
If the answer to the above is yes, why not try another anti-FLAG raised in another animal? If all these fail, try radiolabelled S-methionine labelled IP (yes, I know it is messy and would not be my first option).
Perhaps there is some cross-reactivity. I would recommend to cross-link the anti-FLAG antibody to the Protein A or G sepharose using dimethyl pimelimidate (DMP) (available from Sigma). This is a standard procedure; protocols can be found easily on the internet. The method is quick, efficient, and covalently binds the antibody to the matrix. If you use the cross-linked beads for the IP and finally elute your immunoprecipitate in 100 mM Tris / 0.5% SDS pH 9.0 with vortexing for 30 minutes at room temperature instead of boiling, no antibody should come off. Your blot should be clean.
Alternatively, you can biotinylate your rabbit antibody against the co-eluted protein and detect the specific signal in the blot with streptavidin-HRP (instead of a secondary antibody).
Perhaps there is some cross-reactivity. I would recommend to cross-link the anti-FLAG antibody to the Protein A or G sepharose using dimethyl pimelimidate (DMP) (available from Sigma). This is a standard procedure; protocols can be found easily on the internet. The method is quick, efficient, and covalently binds the antibody to the matrix. If you use the cross-linked beads for the IP and finally elute your immunoprecipitate in 100 mM Tris / 0.5% SDS pH 9.0 with vortexing for 30 minutes at room temperature instead of boiling, no antibody should come off. Your blot should be clean.
Alternatively, you can biotinylate your rabbit antibody against the co-eluted protein and detect the specific signal in the blot with streptavidin-HRP (instead of a secondary antibody).