We don't have a way to calculate that directly in QIIME 2, as far as I am aware. If this is for an SRA submission, perhaps they have some recommendation on how to do this? You might also check with some more general tools for working with fastq files, like FastQC. It's also possible a clever forum user might be able to provide an example of how to do this using Linux built-in tools, which shouldn't be too difficult but I don't have time right now to derive and test a command for doing this.
Maybe this is utterly naive, but if the reads are untrimmed, wouldn't the average spot lenght be 300nt? And, if the reads are trimmed, wouldn't you expect it to be 300 - trim length?
@jwdebelius, I think you may be right. Despite the title of this post (my bad), I was thinking the goal was calculating a total spot length as something like the length of all reads, post-trimming, summed on a per-sample basis.
So that said, @M_F, if using QIIME 2 for read processing, there isn't a direct way to have this computed across all samples post demultiplexing (someone please correct me if I'm forgetting about something here), but the output of qiime demux summarize will provide this information across all samples in the bottom of the second tab. For example (for a single-end data set):