Edit: Misread question. Second try:
No, you can't obtain ARTIQ-6 over Conda, the current legacy version is 7. Older versions than this are no longer built on M-Labs servers and Conda has nowhere to obtain them from. In any case, this wouldn't actually help you. Please understand that artiq_flash
does not and AFAIK never has generated binaries, only flashed them, that is, copied them onto the core device. You need to obtain the binaries somehow regardless.
Previously, the variants you wanted were built by M-Labs and included in the Conda package, so you could access them directly. To reflash ARTIQ-6 you would need to build these binaries yourself.
What hardware are you using? If it's KC705, certain (modern) variant binaries are still available for download on the M-labs Hydra server.