Good to hear so many strawberry growers out there !
Strawberry plants with few or no flowees, might simply be too small or young, a very late variety, perhaps in a cooler than average climate, but low flowering may also suggest too much nitrogen ie soil too rich or too much manure, try feeding with a tomato fertiliser.
And strawbs in baskets, fine, but definitely harder to get a heavy crop - use a big basket and keep them really well watered and fed and you will increase the crop ! good luck!