I would like to know why eggshells are good for flowering plants!
Eggshells, as Kate says above, are mostly calcium, with a bit of lime and protein. Calcium is important to flowering and more particularly fruiting plants, and the lime improves magnesium and alkalinizes the soil, which is good for plants like roses. For instance, Blossom End Rot in tomatoes is caused by a shortage of calcium - but this may be caused by underwatering, which disables the plant from taking up any calcium already present in the soil.
On the other hand, because it's difficult to assess quite how much calcium and lime your plants are getting (depending on the quantity and frequency of application of eggshells) I'm not convinced they're at all useful, preferring instead to use measured doses of plant food appropriate to the plants, and adding the eggshells to the compost heap, which eventually will be added to the soil anyway.
Calcium is not mobile in soils so in order for eggshells to be useful it must first be degraded into little particles, digested by bacteria then washed down to the root level. This takes a while so composting would be more efficient, particularly if you dig your compost in.
In limestone soils and where the ph is above 7 calcium is rarely deficient. It does provide a short lived barrier to slugs if applied in quantity.
You are better off composting your eggshells so that the resulting compost has available calcium.
If you are gardening on acid or poor soils these plants respond well to calcium applications:
apples, broccoli, brussel sprouts, cabbage, carrots, cauliflower, celery, cherries, citrus, conifers, cotton, curcurbits, melons, grapes, legumes, lettuce, peaches, peanuts, pears, peppers, potatoes, tobacco, and tomatoes.