- /æ/ is non-existent in Standard German;
- General British (= GB) /æ/ differs from General American (= GA) /æ/;
- the quality of /e/ a German learner of General British should aim at is but one of many qualities which one can hear in the English-speaking world.
Germans very frequently produce an /æ/ close to the New Zealand (and South African) variant.
As there's hardly any kinaesthetic/proprioceptive information available during the articulation of /æ/ (and many other vowels), it's vital to concentrate on listening for the correct vowel quality in order to become sensitive for it. To hit the right target is a matter of trial and error.
And - do not mix accents! If you've decided on GB you shouldn't say words like France, dance, grass with an /æ/.
And - do not forget that /æ/ is but a convenient label for a variety of actual pronunciations.
And - it's less important to memorise the transcription symbol than to memorise and automatise the proper pronunciation.
And - practise, practise, practise until you are certain your listeners are able to distinguish whether you say "Flesh Gordon" or "Flash Gordon". It can be rather embarrassing if you don't hit the proper target. (If you don't know what I'm talking about, you're an honourable person, but you should search the Internet for the difference between the two expressions.)