I think it would be a good idea to ask the homeowner first. Otherwise, you may come face to face with a dog or something else harmful.
Is it illegal to walk a little bit into the front garden area in others' property and take photos of the flowers there and post them on internet?
no, even i do that but it will be awkward moment when someone is there in the garden and seeing you while taking pictures
Tresspassing is always illegal. Even just a few feet. Never mind that entering private property and taking pics is just rude. Technically they could call the police. Once you pass the property line you are committing a crime. Maybe more than one Tresspassing. Violation of privacy. Would you want strangers tramping through your yard taking pictures of your things? Always ask permission to do things in private property
It is always a good idea to both "Ask Permission" and "Explain Intent" in this regard . . . . For many reason besides the legal ones.
Unless this is Public property that you pay taxes on clear communication is key.
Use your own judgment. The one's I post are from public places not people's yards.
Legally once you cross their property line it criminal trespass in Colorado. "Walk a little bit!" Either you have a really bad camera or your going in more than just a little bit.
Once you've passed the property "threshold" (property boundary line) so to speak and actually enter onto private property you are trespassing .. Legally and morally. That is an "invasion" .. Taking photos without consent, again is another invasion.