Learn Icelandic: Þeir ætla að segja línuna öskrandi. - They are going to say the line, screaming.

It is the present participle of the verb öskra (to scream). In this sentence, it is being used as an adverb of manner to describe how they are saying the line. When present participles are used as adverbs, they are completely uninflected, meaning they never change their endings to match gender or number.

Could I use öskrandi with the verb to be to say "They are screaming" like we do in English?

No, that is a very common trap for English speakers! Icelandic does not use the -andi form to make continuous verb tenses. To say "They are screaming," you would use the continuous construction Þeir eru að öskra. The -andi ending is primarily for making adjectives or, as shown here, adverbs of manner.

Does línuna mean a physical line like on the ground, or a line in a script?

Here it refers to a line of text or dialogue in a script, though the base word lína can also mean a physical line. It is in the accusative case here because it is the direct object of the verb segja (to say), and the -na at the end is the attached definite article, making it "the line".

Why is the sentence using ætla að segja instead of a future tense verb for "will say"?