The sRGB profiles on the ICC have this disclaimer:
To anyone who acknowledges that the file "sRGB_ICC_v4_appearance_beta.icc" is provided "AS IS" WITH NO EXPRESS OR IMPLIED WARRANTY, permission to use, copy and distribute these file for any purpose is hereby granted without fee, provided that the files are not changed including the ICC copyright notice tag, and that the name of ICC shall not be used in advertising or publicity pertaining to distribution of the software without specific, written prior permission. ICC makes no representations about the suitability of this software for any purpose
The sRGB profiles on the ICC have this disclaimer:
To anyone who acknowledges that the file "sRGB_ICC_v4_appearance_beta.icc" is provided "AS IS" WITH NO EXPRESS OR IMPLIED WARRANTY, permission to use, copy and distribute these file for any purpose is hereby granted without fee, provided that the files are not changed including the ICC copyright notice tag, and that the name of ICC shall not be used in advertising or publicity pertaining to distribution of the software without specific, written prior permission. ICC makes no representations about the suitability of this software for any purpose.
So it looks like yes, you can distribute at least these versions of them.
The profile in question is Copyright (c) 1998 Hewlett-Packard Company.
Check your license agreement. License agreements make a clear distinction between embedding and stand-alone distribution of ICC profiles. The former is almost always allowed as that’s part of the purpose of the profile.
There are several sRGB profiles available online under various licensing terms.
Whether you use a JPEG file or another image file, the image compression process should remain more or less the same, but with JPEG images there is a risk of loss of resolution when compressing the images.