Both Uses of

inflexible

in

Jane Eyre

Here the honest but inflexible servant clapped the door to and bolted it within.†
p. 385.7 *

inflexible = not bendable or adaptable

As I walked by his side homeward, I read well in his iron silence all he felt towards me: the disappointment of an austere and despotic nature, which has met resistance where it expected submission — the disapprobation of a cool, inflexible judgment, which has detected in another feelings and views in which it has no power to sympathise: in short, as a man, he would have wished to coerce me into obedience: it was only as a sincere Christian he bore so patiently with my perversity, and allowed so long a space for reflection and repentance.†
p. 472.2

Definition:

not bendable or adaptable

in various senses, including:

not willing to compromise or make concessions -- as when a boss says "Do it my way or you're fired."
not able to adjust well to different conditions -- as of a schedule that cannot be changed
not easily bent without physical damage or injury -- as of brittle steel or person with stiff joints