To sow a chamomile and grass lawn, throw some seeds on bare soil, cover with a little soil, and water. The chamomile that I use is Chamaemulum nobile (Roman Chamomile). This works very well in a lawn with grass. The grass can handle lots of foot traffic, and the chamomile smells great. Every year I put up a paddling pool for summer. It leaves behind a circle of dead grass and bare dirt. This article shows how I remedy this. Follow the slideshow, above, for step-by-step instructions.
For best results keep the soil damp. This may mean watering several times a day for a minute or two. A sprinkler with a timer is your friend! Baby plants have shallow roots which can only reach water near the surface. Allow the new grass and chamomile to grow, until the grass is tall enough that it starts to bend rather than go straight up, then mow. This might be 7cm to 10cm high. Water less often, but for longer. Try 25mm a week (including rain) in temperate regions during the warmer half of the year. Mow on the highest setting until the turf is dense and then lower the mower setting each week until the desired height is achieved. Mowing too short, too early, or too fast, will hurt the baby plants and you may end up with bare patches and weed infiltration. Because chamomile spreads via stolons it will fill gaps. For turf management follow the lawn care link below. The ratio of grass to chamomile will be what it is. You may find that the ratio changes over time as the plant best suited achieves dominance. Chamomile won't produce flowers if mown regularly.
Chamaemelum nobile is an article I've written on the plant along with photos of it in various stages of growth.
Plant a Chamomile Lawn inspired me to try creating a chamomile lawn. A useful article if you want a pure chamomile lawn. It also talks about the different types of chamomile. Jane Wrigglesworth (the author) responds to all the comments on her blog. The comments are also worth reading as she may answer questions that you didn't know that you had.
Organic Lawn Care for the Cheap and Lazy is how I care for my chamomile lawn, and lawns generally.
Chamomile Seeds from Kings Seeds in New Zealand. One packet of 2000 seeds for 15m2 (the area of the pool in the slideshow) is enough. Mix with fine sand, or sugar, to make it easier to broadcast evenly.