KSHS is a Community school and therefore follows the Lincolnshire Admissions Policy. You can see this on the Council's website but basically after children in Care and siblings the places are allocated first to children who live in the designated area for school transport and then in order of distance from the school. The distance criteria is applied in the same fashion whether or not you live in Lincolnshire (it is not permitted to give priority to children in county over those out of county)- thus you would be allocated a place over a Lincolnshire child who lived further away than you do.
The school had a huge number of applications from girls who passed last year and took in an extra class of 30 over its usual numbers last September. This, however, was an exceptional circumstance, not to be repeated as Grammar schools are not generally allowed to expand.
I am afraid that the not very helpful answer to your question about the chances of getting in is that it depends how many girls have passed and applied who live nearer to the school than you do or already have a sister there.
If you do not get allocated a place you need to appeal before the end of March. You can get a booklet explaining the appeals process from the admissions department at Lincolnshire county council. Basically when a school is oversubscribed the appeal is a balancing exercise between the "prejudice", that is damage, to the school in taking an extra pupil and the "prejudice" to the child in not gaining a place there. The arguments you use to support your case will be individual to you but could include medical reasons, social reasons, the curriculum offered at the school allocated as opposed to the school you are appealing for, ease of transport links, journey time, and so on. There are some helpful booklets available via the web either free or at low cost and also books you could borrow or buy to help you prepare your case. The Advisory Centre for Education have one you can download from their website www.ace-ed.org.uk
and there is also a free one available on www.schoolappeals.org.uk
Appeals for a particular school are generally held in a block, most often in the summer term.
Hope this is of some use.