Putting anything non-lighting related on the lighting circuit is bad form. That's not the same as saying that bodgers don't do it, but it's not how these things should be done.
Your second question: Yes, complete BT receiver/amp/speaker modules do exist, but anything small enough to fit in to a standard down-lighter hole is going to have a very small speaker and not much space for any kind of acoustic backbox to try to help load the back to boost what little bass there is. For sound quality then, think "workman's paperback-sized transistor radio"; that kind of thin scratchy annoying sound rather than the modest but warmer tones of a decent BT speaker.
Bose and KEF both do small satellite speaker systems, but they back it up with a sub bass box about the size of an overnight bag. This hidden away somewhere out of sight, but its role is vital in making the sound listenable.
What this means is you're either going to have to make bigger cutouts to install a speaker with a (minimum) 5" bass driver, or you'll end up buying and installing something that turns out to be a white elephant.
Finally, fire safety.
Your downlighters have intumescent seals, or you've fitted fire hoods, right? Right?? Your ceiling speakers need the same.
Hoods to cover 5"~6.5" speakers will set you back £120 a pair. That's extra to what you'll spend on the speakers. This little idea is starting to look expensive.
The next obvious question is whether you can skimp on the hoods. The answer is yes. If your kitchen is entirely separate from the main body of the house and has no living space above it then you're free to do what you want with the ceiling. But if there's a bedroom above, or a cavity for smoke and flames to travel to the main body of the house, then you'd better think twice.
Kitchens are the most common start point for a house fire. Having your insurer tell you your policy is null and void after a claim because something you failed to install helped the fire spread further and faster… well, it doesn't bear thinking about, let alone any other consequences.
If you have £600 to spend then you could do it well enough to be a good system. For a £Grand you could knock it out of the park.
On the other hand, if you were thinking £150~£200 all-in then I would go with a Sonos Play 1 speaker. The app on your phone will connect to the speaker via the house Wi-Fi. Not only will this give you more range and the ability to control all the features of the speaker, but it will sound better than BT too.
The Play speaker will give you access to streaming content without tying up the phone. You'll have voice control too, and if you have a Apple tablet or phone then you can run their room acoustic wizard which really helps dial in the performance.
