Being honest, it's probably better all round to remove the linseed completely and start again using teak oil.
Putting the teak over the lineseed will probably result in the sticky non-drying mess linseed can be prone to.
To remove you'll need turpentine, soapy water and rags.
Pour some turps on a rag and apply to the wood using a circular motion. When you see the Linseed statrting to dissolve leave it sit for around 20minutes for the turps to do it's work.
After 20 mins wash the whole lot down with warm soapy water, scraping off any remaining linseed with a rag.
Let it all dry out again, then redo with teak oil.
Start with two coats, applied at least 6 hours apart (preferably overnight).
Then coat again after 4 months. You can then move to an annual routine (or as required), personnally I give my stuff a coat in the spring as they come out to play and again before I put them to bed at the end of the season.
Have fun