I believe that, because of the change in mount, they will accelerate the upgrade cycle this time and have the flagship ready in 2022.
Possibly. Or, they could compromise and release a flagship R1 in 2023, with development announcement in third quarter 2022.
My uninformed opinion:
With the R3 announcement Canon keeps emphasizing that the 1DxIII will remain the "flagship" camera. This may be simply a marketing strategy to keep 1DxIII sales from cratering, or it could be a recognition that the professional customer base for the 1D series is not itching to switch to mirrorless.
That's not to say that the enthusiast base, which probably accounts for more 1Dx sales than the professional base, doesn't want a mirrorless "pro" camera. That segment does and they will get it with the R3. But, with the R3 in the lineup, Canon may feel little urgency to release an R1 geared to the shrinking pool of professional users. Especially since the professional market is more conservative and was always going to be the last segment to move to mirrorless.
The R3 may become the camera of choice for the lucrative enthusiast market that wants the latest and greatest. It could also become a more affordable option for sports photographers and photojournalists who have to buy their own equipment (which is a lot higher percentage of the total market than it once was.) The R3 can also serve as a test bed for high end professional sports and Olympics photographers, allowing Canon to learn what works and doesn't work for these users. Canon could then concentrate on making the R1 a camera for this much smaller and shrinking base of professional users without feeling any urgency to rush the development -- especially since it's unlikely to be much of a profit generator for Canon. It could be a 2023 camera or it could be a 2024 camera, maintaining the traditional four year Olympic cycle.
It's also entirely possible that we are overestimating Canon's own knowledge of what they plan to do. We are in a new and perilous era for camera manufacturers. The market has been totally disrupted by the COVID-19 pandemic, making it extremely difficult to get a clear reading on where the market is headed. Even without the pandemic, the market was rapidly shifting and shrinking. One side effect of the pandemic that people don't think about is how it has limited the ability of manufacturers to field test equipment. If an R1 is in development, just where do people think it is being tested, given how many professional and college sporting events have been cancelled over the past year. The pandemic has impacted development cycles in ways that we may never know.