I found another sefer which quotes the letter. I don't know if it's quoting the letter in full, but it's more detailed than what you are quoting from Rav Chaim Friedlander. Here is what it says:
ומה שאמרו באבות: 'ואל תרבה שיחה עם האשה, באשתו אמרו קל וחומר באשת חברו, מכאן אמרו חכמים כל המרבה שיחה עם האשה גורם רעה לעצמו ובוטל מדברי תורה וסופו יורש גיהנם' באינו צריך לרצוי מדבר, ולא בשנה ראשונה שצריך להשתדלות התאחגות שזה וכונת היצירה "והיו לבשר אחד". וגרסינן בסוטה 'דרש רבי עקיבא: איש ואשה שזכו שכינה ביניהם, לא זכו אש אוכלתן'
Regarding what is taught in Avos: "Don't talk excessively with a woman, meaning one's wife. All the more so someone else's wife. From here the Sages said: Anyone who talks excessively with a woman causes evil for themselves, wastes time from learning, and in the end will inherent gehenom." That is when a person doesn't need to enhance a relationship. Not so during the first year of marriage, where a person needs to endeavor to become one with their wife. This was the intent of the creation of Man and Woman, as it says "they shall be one flesh". And it is taught in Sotah: Rabbi Akiva expounded: A husband and wife who merit, the Divine Presence rests between them, and if they don't merit, a fire consumes them.
The sefer I was looking at cites Sotah 17a, which indeed is the source for Rabbi Akiva's teaching.
I assume Rav Chaim Friedlander was paraphrasing what the Chazon Ish wrote, as he assumed those reading his kuntres would be familiar with the gemarra.