how to write dynamic elastic search query in NEST C#

Just take a look at what the LessThanOrEquals and LessThan generic extension methods do. Basically, they extend a DateRangeQueryDescriptor of T (in this case, T is a Book), accept a DateMath argument, and return another DateRangeQueryDescriptor. So, we can just break out a function that, depending on the includeEnd flag, returns the correct function to expect the query descriptor.

public IEnumerable<Book> GetBooks(DateTime startTime, DateTime endTime, string author, bool includeEnd)
{
    var dateFilter = includeEnd ?
        // you have to do a little casting for the lambdas to know what type we're returning
        (Func<DateRangeQueryDescriptor<Book>, DateRangeQueryDescriptor<Book>>)
        (q => q.LessThanOrEquals(endTime))
        : q => q.LessThan(endTime);

    return elastic.Search<Book>(s => s
        .Index(IndexName)
        .Query(q => q.Term(book => book.Author, author) &&
                    q.DateRange(i =>
                    {
                        i = i.Field(book => book.Author)
                        .GreaterThanOrEquals(startTime);
                        return dateFilter(i);
                    }
            )))
            .Documents
            .ToArray();
}

To take this idea further, you could write your own extension method:

public static class DateQueryExtensions
{
    public static DateRangeQueryDescriptor<T> LessThanWithOption<T>(this DateRangeQueryDescriptor<T> q, DateMath to, bool includeEnd)
        where T : class
    {
        return includeEnd ? q.LessThanOrEquals(to) : q.LessThan(to);
    }
}

Then you can use it like this:

public IEnumerable<Book> GetBooksUsingExtension(DateTime startTime, DateTime endTime, string author, bool includeEnd)
{
    return elastic.Search<Book>(s => s
       .Index(IndexName)
       .Query(q => q.Term(book => book.Author, author) &&
                   q.DateRange(i => i.Field(book => book.Author)
                       .GreaterThanOrEquals(startTime)
                       .LessThanWithOption(endTime, includeEnd)
                   )))
           .Documents
           .ToArray();

}

Most of the Nest fluent interface extensions operate on query descriptors in a similar manner.