We also did a lot of lying on our chests, or over our shoulders. At 2 months our MCHN suggested that he also needed a bit of time on the floor, since while he was lifting up his head OK (part of the reason for tummy time) he had no sign of the foot-scrabbling that was apparently the other thing that should be developing. He lasted a couple of minutes in front of the floor-to-ceiling-window, watching the tree - and he did that each day for another month or so. Then mysteriously he started to not mind it much first thing after waking up - so he would have a long session then and that was it.
After that poor bub learnt to roll from his back to his tummy - and it took him 2 months to learn to roll the other way. So he got a very large amount of tummy time from 4-6 months...

From the "flat head" point of view, anything that is not lying on their back will be helpful - so your sling or cuddle time is important here.