Patrick, the poppies of Flanders Field are indeed the red Papaver rhoeas, an annual. With a little encouragement they will reseed every year and become a perennial presence in the garden. For my climate the only reliable perennial poppies I've found are Oriental types, but there are some great true red varieties among those. I like growing both because the Orientals bloom when bearded irises are blooming, and P. rhoeas blooms just after, typically through June.
Lyn, I've never tried deadheading P.rhoeas before to extend bloom- I need to try that sometime! I know this works well with lots of plants, just hadn't thought to try it with poppies. Ca. poppies aren't the same genus, but it's certainly worth a try.