"sufferings" is plural though it is uncountable,but how?

"[W]e know that there is no plural form of 'uncountable noun' ..."

Do we really?

[I'm taking this preamble to read 'we know that mass nouns are always singular' in line with the statement below: ' ... the idea that mass nouns are always singular has been part of conventional wisdom ever since Bloomfield (1933)'.]

Peter Lasersohn, in Mass Nouns and Plurals, writes:

[One] issue is whether the term 'mass' should be understood broadly enough to include some morphologically plural examples. Jespersen argued that a wide range of plural nouns were actually mass, including examples such as

victuals, oats, brains (in the sense exemplified in blow out somebody’s brains), dregs, lees, proceeds, measles, mumps, hysterics, blues, creeps, and others.

We may note that these impose plural agreement on the verb, but (under the relevant reading) combine with much rather than many:

(8) a. In this kind of work, brains are less important than guts.

b. It doesn’t take much brains to figure this out.

Here again Bloomfield (1933) introduced a shift in terminology, stipulating that mass nouns “have no plural,” without providing discussion of Jespersen’s examples; the idea that mass nouns are always singular has been part of conventional wisdom ever since.

Plural mass nouns have been periodically rediscovered (McCawley 1975, Gillon 1992 ), and are treated in detail in Ojeda (2005). Some authors (e.g. Gleason 1965: 135) consider such examples to be neither count nor mass, but a third category.

Even if we recognize some morphologically plural examples as mass nouns, it should be noted that they, like morphologically singular mass nouns, lack a number distinction; in these examples it is simply the singular which is “missing” rather than the plural.

I don't think that anyone would reckon the noun clothes, which takes a plural verb, to be a count noun. Wikipedia [tidied] comments:

mass nouns such as "water" or "furniture", with which only singular verb forms are used : the constituent matter is handled in a grammatically nondiscrete way (although it may ["water"] or may not ["furniture"] be etically nondiscrete)

And, though garments can be counted and so 'clothes' is etically discrete, it is not handled as a typical count noun accepting numerals.

Although there are rare examples of 'sufferings' (as indeed for 'furnitures' and 'waters') which show true count behaviour (eg 'The Three Sufferings – Balanced Holistic Weight Management'), the plural mass-noun usage equivalent to 'what he has gone / is going through' is far more common and is almost certainly the intended usage here. Consider: one would do a double-take on seeing say "three trials and tribulations".

"While uncountable nouns do not generally take a plural form, sometimes they may be pluralized when used in a countable sense."**

Uncountable nouns are usually singular, but not always. It's not a catch-all rule by any means, especially when discussing abstract nouns used in the countable sense. Take this example:

He has sympathy for the sufferings of his fellow countrymen.

You can't quantify the suffering of each countryman. Thus, you can't quantify the sufferings of the countrymen either. Nonetheless, each one suffers. So, when the countrymen are considered as a whole, each one's suffering amounts to their sufferings.

Though general rules regarding the countable/uncountable distinction are valid, there are many exceptions and the context is important. Here's a good example:

It's always wrong to take a life [countable singular] because life [uncountable singular] is precious. The lives [uncountable plural] of many have been sadly cut short. That being said, how lucky are cats to have nine lives [countable plural]?