Over on the weeds forum, where you asked the same question, it was explained that a weed killer which kills broad leaved weeds like thistles will also kill your flowers. Pulling, hoeing, mulching and hand forking will work. Thistles are easy to spot and pull. Get them before they seed and you will gradually deplete the seed bank in the soil. Weeding is one of the integral activities of gardening and it helps you learn a lot about your plants by getting down close to your garden.

Well I will tell you the easiest, most effective, and in most cases the most economical way. Hire an experience tractor box blade operator to come out and re-grade the yard. It will take them two hours at most and when finished you are set to go. They can even add amendments if you wish. No need to spray any herbicides, just grade it and be done with it. Otherwise you are looking at hours and hours of back breaking work with mediocre results at best. Around here operators get $125 to $150 per hour with two hour minimum. Best money you will ever spend on your yard.

How much sun does it get?

Going at it chemically, the objective would be to hit it at the time it is storing up energy for winter. This way while it's building starches in the roots for it's next years growth, it mixes in your chemical control and dies instead. Different species of thistles do this at different times of year. Bull thistle is most vulnerable in late fall, Canada Thistles are vulnerable in late spring and early fall. Going at it without chemicals, chopping the plant down before it can get too big consistently forces it to use up it's stored food to try building new leaves. If you take those leaves away before it can actually get a return on investment it eventually starves to death. Oddly, letting it get a little size on it before cutting it down is to your favor. If it loses it's first growth when it's still small, it's only made a small investment. If you chop it when it's four to six inches, that's when it's really invested in the success of those leaves. A slightly more labor intensive option is uprooting. In bull thistles this is a good chance at a kill in one swing, because their taproot is long, but it only has one. Canada Thistle is harder to take on this way, it's root system creeps overground and spreads underground. Trying to rip it up turns one large plant into several small ones. If you're vigilant about cutting back the top growth, this can still work to your benefit, some of the roots won't recover from the trauma. Others will and will send up new shoots, which you can then cut down. If you forget your rounds for a few weeks though, you can end up with several strong plants instead of just one.