Gene expression data is open. Not sure if that's what you need but you can download it the following way:
On Cancer Projects page on the left panel check EXP-S (Sequencing-based Gene Expression) and/or EXP-A (Array-based Gene Expression) in "Available Data Type section". You'll see all projects for which specified data type(s) are available (example)
Then you can download expression data for all donors of one project through data repository: for example current data release has .tsv exp_array.BRCA-US.tsv.gz and exp_seq.BRCA-US.tsv.gz for BRCA-US project
You can also download gene expression data for one donor: on Donors page apply the same filtering as previously metioned (example). When you click on donor ID you'll be taken to donors page where you can click "Download Donor Data" button and select the type(s) of data you want.
Hope this helps.