Comprehensive type schools in, or generally accessible from, Chislehurst:
Coopers, Chislehurst School for Girls (was formerly called Beaverwood School), Kemnal Manor Boys, Bullers Wood Girls, St Thomas More RC, Eltham (Catholic requirements), Bishops Justus CofE in Bromley (40 non faith places plus a change of admission criteria for 2019).
Grammar schools in Bromley borough: Newstead Wood Girls, St Olave's Boys, both in Orpington. Own school test, two tier for St O's.
You can apply for the 4 Bexley Grammar schools over the borough border by taking the Bexley test. One of these grammars is Chislehurst and Sidcup Grammar School (co-ed) which is very popular and very close, in Sidcup. Many children who live in Chislehurst attend. One straight bus ride from Chislehurst.
You can also apply to the Kent grammar schools by taking the Kent Test. Coaches to Wilmington and Dartford schools run through Chislehurst.
Bullers Wood Girls and Chislehurst School for Girls are rated the best comps in Chislehurst by my friends. The new Bullers Wood Boys school is due to open in a temporary site in Bromley but will relocate back to Chislehurst once planning problems have been finalised.
My personal opinion would be for your relative to look at as many schools, their websites and their admissions criteria as possible. Coopers have a test to determine which academic band a student should go into. How they then "set" these bands, I am unsure of.
Hope that helps.