Free fitness app as just bought Apple Watch but had a free 3 month trial on new iPhone. Can I get a further 3 months free now?

No. Sometimes depending on who the offer is coming from (for example, if you bought the watch from Best Buy or another authorized retailer) it may provide an amended free period for “returning subscribers” but it would be less than the full 3 months. But generally if it is the offer directly from Apple it would only be for new subscribers that have not previously used a free trial.