Oh, forgot to say where I am. In southern NJ, just east of Philadelphia (about 10 miles from Philadelphia), in case that makes any difference in any answers.
TIA

Basil will flower as a small seedling. It's the nature of the beast. While it's very young, you can pinch or cut off the flowers as they appear, but as the plant grows (and especially when it's a full-size shrub) you'll need your hedge-cutters to do the job. You could do this every day of your life while the plant is alive! Frankly, the only reason I do it is because with the flowers so profuse, the plant become top-heavy and threatens to pull itself out of the ground.

Otherwise I leave the flowers right where they are. I notice absolutely NO difference in flavour. Perhaps that's because I live in a hot climate which is what basil prefers.

Well, to be clear, I did not see any flowers. Just the very top of the plant growing that 1 inch stalk sort of thing with all the teeny leaves. Questions is, should I go and buy some more basil plants now in the event these aren't going to make it through the season?
If I could figure out how to use my new digital and then figure out how to post a photo, you could actually see what I am talking about:)) Guess I should read the manual!

That sounds like a flower stalk starting up. Why on earth do you think the plant is going to die just because it flowers? If you have warm enough (call it hot!) your plant will do very well indeed. Just while it's very young, pinch out those flowers or beginnings of flowers - that will help the plant become bushy. But once it's mature, removing the flowers is entirely up to you! Basil attracts bees to the garden, which is great if you're growing fruit and veges. Just what you want.

My experience with basil in the past (I have grown it for at least 7 years, every summer), is that once it flowers the leaves get harder and the basil is no longer tender. The flavor changes, and there is less new growth to the plant. I have never seen the basil attempt to flower until August, at least. Just think thks is a little strange, so early in the season.
Since we are discussing basil, is there a 'best' way to pick the leaves? I just pick what I need with no rhyme or reason. My plants usually get tall and thin. To get them more bushy, should I be picking from the sides more often? Seems like I usually take what's near the top.
Thanks for helping.

If you prune a plant from the top, you will encourage a shorter, 'fatter', squat plant.

If you prune a plant from the sides, you'll encourage a tall, thin plant.

If you prune it all over, you've got a nice round ball.

With basil, I don't pick leaves. I use a hedge-trimmer and trim it all over. I rub the leaves off what I want, and use the rest for mulch. My basils get to a decent size, you see.

I honestly think the flowering/leaf thing with basil is entirely because people are trying to grow it in the wrong places! I mean, my basils flower profusely from a tender age, and I could spend my entire life chopping off the flowers. Yet the flavour of the leaves is superb. Perhaps in cooler climates, where their isn't enough sun and heat to produce all those essential oils, the flavour does go 'off' a bit once the plant flowers.

I'm with you, even my first experience growing basil, I noticed NO change in flavor when parts of the plant started flowering. Perhaps it IS all about climate. It gets HOT here and stays that way SPRING and SUMMER...sometimes quite warm through the fall. Heck....I remember a Christmas or two where you could wear shorts outside.

Hebolistic, there may be little change in flavor but the stems will become woody and stringy when those flowers open. Up until that time the buds are excellent for pesto, etc.

One Restaurant chef/owner chastised me for over an hour about how basil should be picked. I listened well since he had previously purchased hundreds of pounds of tips from me. If when you break off the tip it strings along the stem then you need to rebreak higher on that stem. Try chopping the lower stem sections in a blender. It will make a stringy mess that nobody will want for pesto.

Dry weather will affect amount of usable tip more than anything else. Although basil loves heat it needs soil moisture to produce lush new growth.

Unopened buds are great to use for pesto, etc. They actually makeup a large portion of the usable tip weight. But once those flowers open all you can do with those tips is attract bees and beetles.

Made the mistake of introducing paying mantis eggs to my garden and basil. Once they hatched and matured, they would spen a whole day sitting on the basil, just waiting for a bee to come along and head for the flowers. Needless to say the praying mantis was huge. I tried relocating them to another part of the garden where they could have done more good work, but they seemed to like to stay on the basil. After seeing them eating the poor unsuspecting bees, I figured that the mantis was not as beneficial as I had hoped for.