I have an 1980ies steel road bike which I used to ride clipless pedals on. I have recently switched to platform pedals for commuting and found out that when I'm coasting and move my feet left and right, I can flex the frame a little bit. The flex is so strong that I can tell only by looking at it that the BB is not aligned centrally under the top tube / seat tube. When I quit the pressure, everything goes back to normal again. Steel frames are known to have some flex, but is this normal?
It's hard to tell how much flexing is happening when you're on the bike due to your movement when pedaling, particularly if you're not smooth.
The answer is "some" (all frames will flex a bit when you ride), but putting a number or picture to it would depend to some extent on how much weight and force you have on the bike and the frame type and stuff too. For example, a 300 pound rider can probably get the same frame to flex a lot more easily than a 100 pound rider (assuming they fit, etc.)
I'd also check is if the frame has any damage (e.g. cracks, dents, etc.) that is causing it to flex more than normal.