I flare up easily when my spouse corrects me. How can I learn to accept criticism?

Begin by separating yourself from the mistake: a comment about an action is not an attack on your dignity.
The Prophet ﷺ defined arrogance as rejecting the truth and looking down on people (Sahih Muslim, Kitab al-Iman). So rejecting a correct criticism simply because it comes from one's spouse falls under a blameworthy trait. An example often mentioned is ʿUmar al-Khattab r.a., who accepted correction from his people and even said may Allah have mercy on the one who shows me my faults. Practical steps: listen to the end, repeat back what you understood, ask for time if emotions run high, and reply once calm. The one giving the criticism must also choose a good time and kind words. See Emotional communication and how to give advice.