There are some plants that can tolerate poorly drained soil.

There are quite a few. For example, http://www.prairienursery.com/
has their catalog sorted by soil type, with sections for "clay",
"sand", etc, and there are similar native plant catalogs/lists in
other areas. For the flower garden I'd give this a try (unless you
really have your heart set on flowers you already know or have picked
out).

The vegetable garden is another matter (well, unless you really want
to expand your horizons by eating things you haven't tried eating
before). I'm not sure why the questioner wrote off raised beds so
fast.

Amending the soil is an option, but you need to add a lot of material
(as much as you'd put into a raised bed, if you want a rule of
thumb). So see what kind of organic matter you can buy/acquire locally
and cheaply by the truckload (for example, straw, compost, manure,
maybe some processing "waste" like seed hulls of some kind). And/or
think in terms of small areas. Setting up fancy drainage systems
(tiles, French drains, etc) can be done but is only peripherally
related to whether the soil itself is retaining moisture.